The swirlprismatodiminished rectified hexacosichoron or spidrox , also known as the prismantiprismoidal transitional didecafold icosidodecaswirlchoron , is a convex scaliform polychoron. It consists of 120 pentagonal prisms , 120 pentagonal antiprisms , and 600 square pyramids . 2 pentagonal antiprisms, 2 pentagonal prisms, and 5 square pyramids join at each vertex.
It can be constructed by diminishing the rectified hexacosichoron , specifically by removing the 120 vertices of an inscribed hexacosichoron . As a result every icosahedral cell of the rectified hexacosichoron gets diminished down to a pentagonal antiprism, while every octahedral cell gets diminished down to a square pyramid. The pentagonal prism cells are the vertex figures under the removed vertices.
A swirlprismatodiminished rectified hexacosichoron of edge length 1 has vertex coordinates given by:
(
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{\displaystyle \left(0,\,0,\,\pm {\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {3+{\sqrt {5}}}{2}}\right),}
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3
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2
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{\displaystyle \left(0,\,0,\,\pm {\frac {3+{\sqrt {5}}}{2}},\,\pm {\frac {1+{\sqrt {5}}}{2}}\right),}
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1
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2
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0
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3
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{\displaystyle \left(0,\,\pm {\frac {1+{\sqrt {5}}}{2}},\,0,\,\pm {\frac {3+{\sqrt {5}}}{2}}\right),}
(
0
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1
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2
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−
3
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5
2
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0
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{\displaystyle \left(0,\,-{\frac {1+{\sqrt {5}}}{2}},\,-{\frac {3+{\sqrt {5}}}{2}},\,0\right),}
(
0
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1
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5
2
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3
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0
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{\displaystyle \left(0,\,{\frac {1+{\sqrt {5}}}{2}},\,{\frac {3+{\sqrt {5}}}{2}},\,0\right),}
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3
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5
2
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0
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1
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)
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{\displaystyle \left(0,\,\pm {\frac {3+{\sqrt {5}}}{2}},\,0,\,\pm {\frac {1+{\sqrt {5}}}{2}}\right),}
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0
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3
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5
2
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1
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5
2
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0
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{\displaystyle \left(0,\,-{\frac {3+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{2}},\,0\right),}
(
0
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3
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5
2
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−
1
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5
2
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0
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{\displaystyle \left(0,\,{\frac {3+{\sqrt {5}}}{2}},\,-{\frac {1+{\sqrt {5}}}{2}},\,0\right),}
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−
1
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5
2
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0
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0
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3
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{\displaystyle \left(-{\frac {1+{\sqrt {5}}}{2}},\,0,\,0,\,{\frac {3+{\sqrt {5}}}{2}}\right),}
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1
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0
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0
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3
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{\displaystyle \left({\frac {1+{\sqrt {5}}}{2}},\,0,\,0,\,-{\frac {3+{\sqrt {5}}}{2}}\right),}
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1
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2
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0
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2
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0
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{\displaystyle \left(\pm {\frac {1+{\sqrt {5}}}{2}},\,0,\,\pm {\frac {3+{\sqrt {5}}}{2}},\,0\right),}
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1
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5
2
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±
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5
2
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0
,
0
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{\displaystyle \left(\pm {\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {3+{\sqrt {5}}}{2}},\,0,\,0\right),}
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3
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2
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0
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{\displaystyle \left(-{\frac {3+{\sqrt {5}}}{2}},\,0,\,0,\,-{\frac {1+{\sqrt {5}}}{2}}\right),}
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2
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0
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0
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{\displaystyle \left({\frac {3+{\sqrt {5}}}{2}},\,0,\,0,\,{\frac {1+{\sqrt {5}}}{2}}\right),}
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2
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0
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{\displaystyle \left(\pm {\frac {3+{\sqrt {5}}}{2}},\,0,\,\pm {\frac {1+{\sqrt {5}}}{2}},\,0\right),}
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3
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2
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5
2
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0
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{\displaystyle \left(\pm {\frac {3+{\sqrt {5}}}{2}},\,\pm {\frac {1+{\sqrt {5}}}{2}},\,0,\,0\right),}
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0
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{\displaystyle \left(0,\,-{\frac {1}{2}},\,-{\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {5+3{\sqrt {5}}}{4}}\right),}
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1
2
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1
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{\displaystyle \left(0,\,{\frac {1}{2}},\,{\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {5+3{\sqrt {5}}}{4}}\right),}
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1
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5
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{\displaystyle \left(0,\,\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {5+3{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}}\right),}
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{\displaystyle \left(0,\,\pm {\frac {5+3{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {5}}}{4}}\right),}
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{\displaystyle \left(-{\frac {1}{2}},\,0,\,\pm {\frac {5+3{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{4}}\right),}
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{\displaystyle \left({\frac {1}{2}},\,0,\,\pm {\frac {5+3{\sqrt {5}}}{4}},\,-{\frac {1+{\sqrt {5}}}{4}}\right),}
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{\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {5}}}{4}},\,0,\,\pm {\frac {5+3{\sqrt {5}}}{4}}\right),}
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{\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {5+3{\sqrt {5}}}{4}},\,\pm {\frac {1+{\sqrt {5}}}{4}},\,0\right),}
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{\displaystyle \left(\pm {\frac {1+{\sqrt {5}}}{4}}),\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {5+3{\sqrt {5}}}{4}}\right),}
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{\displaystyle \left(\pm {\frac {1+{\sqrt {5}}}{4}}),\,\pm {\frac {1}{2}},\,\pm {\frac {5+3{\sqrt {5}}}{4}},\,0\right),}
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{\displaystyle \left(-{\frac {1+{\sqrt {5}}}{4}}),\,\pm {\frac {5+3{\sqrt {5}}}{4}},\,0,\,-{\frac {1}{2}}\right),}
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{\displaystyle \left({\frac {1+{\sqrt {5}}}{4}}),\,\pm {\frac {5+3{\sqrt {5}}}{4}},\,0,\,{\frac {1}{2}}\right),}
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{\displaystyle \left(\pm {\frac {5+3{\sqrt {5}}}{4}},\,0,\,\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}}\right),}
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{\displaystyle \left(\pm {\frac {5+3{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1+{\sqrt {5}}}{4}}\right),}
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{\displaystyle \left(\pm {\frac {5+3{\sqrt {5}}}{4}},\,-{\frac {1+{\sqrt {5}}}{4}},\,{\frac {1}{2}},\,0\right),}
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{\displaystyle \left(\pm {\frac {5+3{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{4}},\,-{\frac {1}{2}},\,0\right),}
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{\displaystyle \left(0,\,-{\frac {3+{\sqrt {5}}}{4}},\,-{\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {5+{\sqrt {5}}}{4}}\right),}
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{\displaystyle \left(0,\,{\frac {3+{\sqrt {5}}}{4}},\,{\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {5+{\sqrt {5}}}{4}}\right),}
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{\displaystyle \left(0,\,\pm {\frac {5+{\sqrt {5}}}{4}},\,\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {2+{\sqrt {5}}}{2}}\right),}
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{\displaystyle \left(0,\,\pm {\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {5+{\sqrt {5}}}{4}},\,\pm {\frac {3+{\sqrt {5}}}{4}}\right),}
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{\displaystyle \left(-{\frac {3+{\sqrt {5}}}{4}},\,0,\,\pm {\frac {5+{\sqrt {5}}}{4}},\,{\frac {2+{\sqrt {5}}}{2}}\right),}
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0
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2
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{\displaystyle \left({\frac {3+{\sqrt {5}}}{4}},\,0,\,\pm {\frac {5+{\sqrt {5}}}{4}},\,-{\frac {2+{\sqrt {5}}}{2}}\right),}
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±
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5
4
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±
5
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5
2
,
0
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{\displaystyle \left(\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {5+{\sqrt {5}}}{4}},\,\pm {\frac {2+{\sqrt {5}}}{2}},\,0\right),}
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5
4
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±
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{\displaystyle \left(\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {2+{\sqrt {5}}}{2}},\,0,\,\pm {\frac {5+{\sqrt {5}}}{4}}\right),}
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±
5
+
5
4
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0
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±
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+
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2
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±
3
+
5
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)
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{\displaystyle \left(\pm {\frac {5+{\sqrt {5}}}{4}},\,0,\,\pm {\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {3+{\sqrt {5}}}{4}}\right),}
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±
5
+
5
4
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±
3
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4
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0
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±
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+
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)
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{\displaystyle \left(\pm {\frac {5+{\sqrt {5}}}{4}},\,\pm {\frac {3+{\sqrt {5}}}{4}},\,0,\,\pm {\frac {2+{\sqrt {5}}}{2}}\right),}
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±
5
+
5
4
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−
2
+
5
2
,
3
+
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4
,
0
)
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{\displaystyle \left(\pm {\frac {5+{\sqrt {5}}}{4}},\,-{\frac {2+{\sqrt {5}}}{2}},\,{\frac {3+{\sqrt {5}}}{4}},\,0\right),}
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±
5
+
5
4
,
2
+
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2
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−
3
+
5
4
,
0
)
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{\displaystyle \left(\pm {\frac {5+{\sqrt {5}}}{4}},\,{\frac {2+{\sqrt {5}}}{2}},\,-{\frac {3+{\sqrt {5}}}{4}},\,0\right),}
(
±
2
+
5
2
,
0
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+
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4
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±
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+
5
4
)
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{\displaystyle \left(\pm {\frac {2+{\sqrt {5}}}{2}},\,0,\,\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {5+{\sqrt {5}}}{4}}\right),}
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±
2
+
5
2
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±
3
+
5
4
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±
5
+
5
4
,
0
)
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{\displaystyle \left(\pm {\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {5+{\sqrt {5}}}{4}},\,0\right),}
(
−
2
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5
2
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±
5
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5
4
,
0
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−
3
+
5
4
)
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{\displaystyle \left(-{\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {5+{\sqrt {5}}}{4}},\,0,\,-{\frac {3+{\sqrt {5}}}{4}}\right),}
(
2
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±
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)
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{\displaystyle \left({\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {5+{\sqrt {5}}}{4}},\,0,\,{\frac {3+{\sqrt {5}}}{4}}\right),}
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−
1
2
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−
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±
2
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5
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2
+
5
2
)
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{\displaystyle \left(-{\frac {1}{2}},\,-{\frac {1}{2}},\,\pm {\frac {2+{\sqrt {5}}}{2}},\,-{\frac {2+{\sqrt {5}}}{2}}\right),}
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−
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1
2
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2
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)
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{\displaystyle \left(-{\frac {1}{2}},\,{\frac {1}{2}},\,-{\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {2+{\sqrt {5}}}{2}}\right),}
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−
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2
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1
2
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2
+
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2
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−
2
+
5
2
)
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{\displaystyle \left(-{\frac {1}{2}},\,{\frac {1}{2}},\,{\frac {2+{\sqrt {5}}}{2}},\,-{\frac {2+{\sqrt {5}}}{2}}\right),}
(
1
2
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±
1
2
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−
2
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5
2
,
2
+
5
2
)
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{\displaystyle \left({\frac {1}{2}},\,\pm {\frac {1}{2}},\,-{\frac {2+{\sqrt {5}}}{2}},\,{\frac {2+{\sqrt {5}}}{2}}\right),}
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1
2
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−
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2
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2
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2
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+
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2
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{\displaystyle \left({\frac {1}{2}},\,-{\frac {1}{2}},\,{\frac {2+{\sqrt {5}}}{2}},\,-{\frac {2+{\sqrt {5}}}{2}}\right),}
(
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2
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1
2
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2
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+
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2
)
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{\displaystyle \left({\frac {1}{2}},\,{\frac {1}{2}},\,-{\frac {2+{\sqrt {5}}}{2}},\,-{\frac {2+{\sqrt {5}}}{2}}\right),}
(
1
2
,
1
2
,
2
+
5
2
,
2
+
5
2
)
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{\displaystyle \left({\frac {1}{2}},\,{\frac {1}{2}},\,{\frac {2+{\sqrt {5}}}{2}},\,{\frac {2+{\sqrt {5}}}{2}}\right),}
(
±
1
2
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−
2
+
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2
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−
1
2
,
±
2
+
5
2
)
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{\displaystyle \left(\pm {\frac {1}{2}},\,-{\frac {2+{\sqrt {5}}}{2}},\,-{\frac {1}{2}},\,\pm {\frac {2+{\sqrt {5}}}{2}}\right),}
(
±
1
2
,
2
+
5
2
,
1
2
,
2
+
5
2
)
,
{\displaystyle \left(\pm {\frac {1}{2}},\,{\frac {2+{\sqrt {5}}}{2}},\,{\frac {1}{2}},\,{\frac {2+{\sqrt {5}}}{2}}\right),}
(
−
1
2
,
±
2
+
5
2
,
1
2
,
−
2
+
5
2
)
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{\displaystyle \left(-{\frac {1}{2}},\,\pm {\frac {2+{\sqrt {5}}}{2}},\,{\frac {1}{2}},\,-{\frac {2+{\sqrt {5}}}{2}}\right),}
(
−
1
2
,
2
+
5
2
,
−
1
2
,
−
2
+
5
2
)
,
{\displaystyle \left(-{\frac {1}{2}},\,{\frac {2+{\sqrt {5}}}{2}},\,-{\frac {1}{2}},\,-{\frac {2+{\sqrt {5}}}{2}}\right),}
(
1
2
,
−
2
+
5
2
,
1
2
,
2
+
5
2
)
,
{\displaystyle \left({\frac {1}{2}},\,-{\frac {2+{\sqrt {5}}}{2}},\,{\frac {1}{2}},\,{\frac {2+{\sqrt {5}}}{2}}\right),}
(
1
2
,
2
+
5
2
,
−
1
2
,
2
+
5
2
)
,
{\displaystyle \left({\frac {1}{2}},\,{\frac {2+{\sqrt {5}}}{2}},\,-{\frac {1}{2}},\,{\frac {2+{\sqrt {5}}}{2}}\right),}
(
1
2
,
2
+
5
2
,
1
2
,
−
2
+
5
2
)
,
{\displaystyle \left({\frac {1}{2}},\,{\frac {2+{\sqrt {5}}}{2}},\,{\frac {1}{2}},\,-{\frac {2+{\sqrt {5}}}{2}}\right),}
(
±
1
2
,
±
2
+
5
2
,
±
2
+
5
2
,
±
1
2
)
,
{\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {1}{2}}\right),}
(
±
2
+
5
2
,
±
1
2
,
±
1
2
,
±
2
+
5
2
)
,
{\displaystyle \left(\pm {\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {2+{\sqrt {5}}}{2}}\right),}
(
±
2
+
5
2
,
−
1
2
,
2
+
5
2
,
−
1
2
)
,
{\displaystyle \left(\pm {\frac {2+{\sqrt {5}}}{2}},\,-{\frac {1}{2}},\,{\frac {2+{\sqrt {5}}}{2}},\,-{\frac {1}{2}}\right),}
(
−
2
+
5
2
,
−
1
2
,
±
2
+
5
2
,
1
2
)
,
{\displaystyle \left(-{\frac {2+{\sqrt {5}}}{2}},\,-{\frac {1}{2}},\,\pm {\frac {2+{\sqrt {5}}}{2}},\,{\frac {1}{2}}\right),}
(
−
2
+
5
2
,
1
2
,
−
2
+
5
2
,
±
1
2
)
,
{\displaystyle \left(-{\frac {2+{\sqrt {5}}}{2}},\,{\frac {1}{2}},\,-{\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {1}{2}}\right),}
(
−
2
+
5
2
,
1
2
,
2
+
5
2
,
1
2
)
,
{\displaystyle \left(-{\frac {2+{\sqrt {5}}}{2}},\,{\frac {1}{2}},\,{\frac {2+{\sqrt {5}}}{2}},\,{\frac {1}{2}}\right),}
(
2
+
5
2
,
±
1
2
,
−
2
+
5
2
,
−
1
2
)
,
{\displaystyle \left({\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {1}{2}},\,-{\frac {2+{\sqrt {5}}}{2}},\,-{\frac {1}{2}}\right),}
(
2
+
5
2
,
−
1
2
,
2
+
5
2
,
1
2
)
,
{\displaystyle \left({\frac {2+{\sqrt {5}}}{2}},\,-{\frac {1}{2}},\,{\frac {2+{\sqrt {5}}}{2}},\,{\frac {1}{2}}\right),}
(
2
+
5
2
,
1
2
,
−
2
+
5
2
,
1
2
)
,
{\displaystyle \left({\frac {2+{\sqrt {5}}}{2}},\,{\frac {1}{2}},\,-{\frac {2+{\sqrt {5}}}{2}},\,{\frac {1}{2}}\right),}
(
2
+
5
2
,
1
2
,
2
+
5
2
,
−
1
2
)
,
{\displaystyle \left({\frac {2+{\sqrt {5}}}{2}},\,{\frac {1}{2}},\,{\frac {2+{\sqrt {5}}}{2}},\,-{\frac {1}{2}}\right),}
(
±
2
+
5
2
,
−
2
+
5
2
,
−
1
2
,
±
1
2
)
,
{\displaystyle \left(\pm {\frac {2+{\sqrt {5}}}{2}},\,-{\frac {2+{\sqrt {5}}}{2}},\,-{\frac {1}{2}},\,\pm {\frac {1}{2}}\right),}
(
±
2
+
5
2
,
2
+
5
2
,
1
2
,
−
1
2
)
,
{\displaystyle \left(\pm {\frac {2+{\sqrt {5}}}{2}},\,{\frac {2+{\sqrt {5}}}{2}},\,{\frac {1}{2}},\,-{\frac {1}{2}}\right),}
(
−
2
+
5
2
,
±
2
+
5
2
,
1
2
,
1
2
)
,
{\displaystyle \left(-{\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {2+{\sqrt {5}}}{2}},\,{\frac {1}{2}},\,{\frac {1}{2}}\right),}
(
−
2
+
5
2
,
2
+
5
2
,
−
1
2
,
1
2
)
,
{\displaystyle \left(-{\frac {2+{\sqrt {5}}}{2}},\,{\frac {2+{\sqrt {5}}}{2}},\,-{\frac {1}{2}},\,{\frac {1}{2}}\right),}
(
2
+
5
2
,
−
2
+
5
2
,
1
2
,
−
1
2
)
,
{\displaystyle \left({\frac {2+{\sqrt {5}}}{2}},\,-{\frac {2+{\sqrt {5}}}{2}},\,{\frac {1}{2}},\,-{\frac {1}{2}}\right),}
(
2
+
5
2
,
2
+
5
2
,
−
1
2
,
−
1
2
)
,
{\displaystyle \left({\frac {2+{\sqrt {5}}}{2}},\,{\frac {2+{\sqrt {5}}}{2}},\,-{\frac {1}{2}},\,-{\frac {1}{2}}\right),}
(
2
+
5
2
,
2
+
5
2
,
1
2
,
1
2
)
,
{\displaystyle \left({\frac {2+{\sqrt {5}}}{2}},\,{\frac {2+{\sqrt {5}}}{2}},\,{\frac {1}{2}},\,{\frac {1}{2}}\right),}
(
±
1
2
,
±
1
+
5
4
,
±
3
+
5
2
,
±
3
+
5
4
)
,
{\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {3+{\sqrt {5}}}{2}},\,\pm {\frac {3+{\sqrt {5}}}{4}}\right),}
(
±
1
2
,
−
3
+
5
4
,
1
+
5
4
,
−
3
+
5
2
)
,
{\displaystyle \left(\pm {\frac {1}{2}},\,-{\frac {3+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{4}},\,-{\frac {3+{\sqrt {5}}}{2}}\right),}
(
−
1
2
,
−
3
+
5
4
,
±
1
+
5
4
,
3
+
5
2
)
,
{\displaystyle \left(-{\frac {1}{2}},\,-{\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {1+{\sqrt {5}}}{4}},\,{\frac {3+{\sqrt {5}}}{2}}\right),}
(
−
1
2
,
3
+
5
4
,
−
1
+
5
4
,
±
3
+
5
2
)
,
{\displaystyle \left(-{\frac {1}{2}},\,{\frac {3+{\sqrt {5}}}{4}},\,-{\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {3+{\sqrt {5}}}{2}}\right),}
(
−
1
2
,
3
+
5
4
,
1
+
5
4
,
3
+
5
2
)
,
{\displaystyle \left(-{\frac {1}{2}},\,{\frac {3+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{4}},\,{\frac {3+{\sqrt {5}}}{2}}\right),}
(
1
2
,
±
3
+
5
4
,
−
1
+
5
4
,
−
3
+
5
2
)
,
{\displaystyle \left({\frac {1}{2}},\,\pm {\frac {3+{\sqrt {5}}}{4}},\,-{\frac {1+{\sqrt {5}}}{4}},\,-{\frac {3+{\sqrt {5}}}{2}}\right),}
(
1
2
,
−
3
+
5
4
,
1
+
5
4
,
3
+
5
2
)
,
{\displaystyle \left({\frac {1}{2}},\,-{\frac {3+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{4}},\,{\frac {3+{\sqrt {5}}}{2}}\right),}
(
1
2
,
3
+
5
4
,
−
1
+
5
4
,
3
+
5
2
)
,
{\displaystyle \left({\frac {1}{2}},\,{\frac {3+{\sqrt {5}}}{4}},\,-{\frac {1+{\sqrt {5}}}{4}},\,{\frac {3+{\sqrt {5}}}{2}}\right),}
(
1
2
,
3
+
5
4
,
1
+
5
4
,
−
3
+
5
2
)
,
{\displaystyle \left({\frac {1}{2}},\,{\frac {3+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{4}},\,-{\frac {3+{\sqrt {5}}}{2}}\right),}
(
±
1
2
,
−
3
+
5
2
,
−
3
+
5
4
,
±
1
+
5
4
)
,
{\displaystyle \left(\pm {\frac {1}{2}},\,-{\frac {3+{\sqrt {5}}}{2}},\,-{\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {1+{\sqrt {5}}}{4}}\right),}
(
±
1
2
,
3
+
5
2
,
3
+
5
4
,
−
1
+
5
4
)
,
{\displaystyle \left(\pm {\frac {1}{2}},\,{\frac {3+{\sqrt {5}}}{2}},\,{\frac {3+{\sqrt {5}}}{4}},\,-{\frac {1+{\sqrt {5}}}{4}}\right),}
(
−
1
2
,
±
3
+
5
2
,
3
+
5
4
,
1
+
5
4
)
,
{\displaystyle \left(-{\frac {1}{2}},\,\pm {\frac {3+{\sqrt {5}}}{2}},\,{\frac {3+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{4}}\right),}
(
−
1
2
,
3
+
5
2
,
−
3
+
5
4
,
1
+
5
4
)
,
{\displaystyle \left(-{\frac {1}{2}},\,{\frac {3+{\sqrt {5}}}{2}},\,-{\frac {3+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{4}}\right),}
(
1
2
,
−
3
+
5
2
,
3
+
5
4
,
−
1
+
5
4
)
,
{\displaystyle \left({\frac {1}{2}},\,-{\frac {3+{\sqrt {5}}}{2}},\,{\frac {3+{\sqrt {5}}}{4}},\,-{\frac {1+{\sqrt {5}}}{4}}\right),}
(
1
2
,
3
+
5
2
,
−
3
+
5
4
,
−
1
+
5
4
)
,
{\displaystyle \left({\frac {1}{2}},\,{\frac {3+{\sqrt {5}}}{2}},\,-{\frac {3+{\sqrt {5}}}{4}},\,-{\frac {1+{\sqrt {5}}}{4}}\right),}
(
1
2
,
3
+
5
2
,
3
+
5
4
,
1
+
5
4
)
,
{\displaystyle \left({\frac {1}{2}},\,{\frac {3+{\sqrt {5}}}{2}},\,{\frac {3+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{4}}\right),}
(
±
1
+
5
4
)
,
±
1
2
,
±
3
+
5
4
,
±
3
+
5
2
)
,
{\displaystyle \left(\pm {\frac {1+{\sqrt {5}}}{4}}),\,\pm {\frac {1}{2}},\,\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {3+{\sqrt {5}}}{2}}\right),}
(
±
1
+
5
4
)
,
−
3
+
5
4
,
3
+
5
2
,
1
2
)
,
{\displaystyle \left(\pm {\frac {1+{\sqrt {5}}}{4}}),\,-{\frac {3+{\sqrt {5}}}{4}},\,{\frac {3+{\sqrt {5}}}{2}},\,{\frac {1}{2}}\right),}
(
−
1
+
5
4
)
,
−
3
+
5
4
,
±
3
+
5
2
,
−
1
2
)
,
{\displaystyle \left(-{\frac {1+{\sqrt {5}}}{4}}),\,-{\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {3+{\sqrt {5}}}{2}},\,-{\frac {1}{2}}\right),}
(
−
1
+
5
4
)
,
3
+
5
4
,
−
3
+
5
2
,
±
1
2
)
,
{\displaystyle \left(-{\frac {1+{\sqrt {5}}}{4}}),\,{\frac {3+{\sqrt {5}}}{4}},\,-{\frac {3+{\sqrt {5}}}{2}},\,\pm {\frac {1}{2}}\right),}
(
−
1
+
5
4
)
,
3
+
5
4
,
3
+
5
2
,
−
1
2
)
,
{\displaystyle \left(-{\frac {1+{\sqrt {5}}}{4}}),\,{\frac {3+{\sqrt {5}}}{4}},\,{\frac {3+{\sqrt {5}}}{2}},\,-{\frac {1}{2}}\right),}
(
1
+
5
4
)
,
±
3
+
5
4
,
−
3
+
5
2
,
1
2
)
,
{\displaystyle \left({\frac {1+{\sqrt {5}}}{4}}),\,\pm {\frac {3+{\sqrt {5}}}{4}},\,-{\frac {3+{\sqrt {5}}}{2}},\,{\frac {1}{2}}\right),}
(
1
+
5
4
)
,
−
3
+
5
4
,
3
+
5
2
,
−
1
2
)
,
{\displaystyle \left({\frac {1+{\sqrt {5}}}{4}}),\,-{\frac {3+{\sqrt {5}}}{4}},\,{\frac {3+{\sqrt {5}}}{2}},\,-{\frac {1}{2}}\right),}
(
1
+
5
4
)
,
3
+
5
4
,
−
3
+
5
2
,
−
1
2
)
,
{\displaystyle \left({\frac {1+{\sqrt {5}}}{4}}),\,{\frac {3+{\sqrt {5}}}{4}},\,-{\frac {3+{\sqrt {5}}}{2}},\,-{\frac {1}{2}}\right),}
(
1
+
5
4
)
,
3
+
5
4
,
3
+
5
2
,
1
2
)
,
{\displaystyle \left({\frac {1+{\sqrt {5}}}{4}}),\,{\frac {3+{\sqrt {5}}}{4}},\,{\frac {3+{\sqrt {5}}}{2}},\,{\frac {1}{2}}\right),}
(
±
1
+
5
4
)
,
−
3
+
5
2
,
1
2
,
−
3
+
5
4
)
,
{\displaystyle \left(\pm {\frac {1+{\sqrt {5}}}{4}}),\,-{\frac {3+{\sqrt {5}}}{2}},\,{\frac {1}{2}},\,-{\frac {3+{\sqrt {5}}}{4}}\right),}
(
−
1
+
5
4
)
,
−
3
+
5
2
,
±
1
2
,
3
+
5
4
)
,
{\displaystyle \left(-{\frac {1+{\sqrt {5}}}{4}}),\,-{\frac {3+{\sqrt {5}}}{2}},\,\pm {\frac {1}{2}},\,{\frac {3+{\sqrt {5}}}{4}}\right),}
(
−
1
+
5
4
)
,
3
+
5
2
,
−
1
2
,
±
3
+
5
4
)
,
{\displaystyle \left(-{\frac {1+{\sqrt {5}}}{4}}),\,{\frac {3+{\sqrt {5}}}{2}},\,-{\frac {1}{2}},\,\pm {\frac {3+{\sqrt {5}}}{4}}\right),}
(
−
1
+
5
4
)
,
3
+
5
2
,
1
2
,
3
+
5
4
)
,
{\displaystyle \left(-{\frac {1+{\sqrt {5}}}{4}}),\,{\frac {3+{\sqrt {5}}}{2}},\,{\frac {1}{2}},\,{\frac {3+{\sqrt {5}}}{4}}\right),}
(
1
+
5
4
)
,
±
3
+
5
2
,
−
1
2
,
−
3
+
5
4
)
,
{\displaystyle \left({\frac {1+{\sqrt {5}}}{4}}),\,\pm {\frac {3+{\sqrt {5}}}{2}},\,-{\frac {1}{2}},\,-{\frac {3+{\sqrt {5}}}{4}}\right),}
(
1
+
5
4
)
,
−
3
+
5
2
,
1
2
,
3
+
5
4
)
,
{\displaystyle \left({\frac {1+{\sqrt {5}}}{4}}),\,-{\frac {3+{\sqrt {5}}}{2}},\,{\frac {1}{2}},\,{\frac {3+{\sqrt {5}}}{4}}\right),}
(
1
+
5
4
)
,
3
+
5
2
,
−
1
2
,
3
+
5
4
)
,
{\displaystyle \left({\frac {1+{\sqrt {5}}}{4}}),\,{\frac {3+{\sqrt {5}}}{2}},\,-{\frac {1}{2}},\,{\frac {3+{\sqrt {5}}}{4}}\right),}
(
1
+
5
4
)
,
3
+
5
2
,
1
2
,
−
3
+
5
4
)
,
{\displaystyle \left({\frac {1+{\sqrt {5}}}{4}}),\,{\frac {3+{\sqrt {5}}}{2}},\,{\frac {1}{2}},\,-{\frac {3+{\sqrt {5}}}{4}}\right),}
(
±
3
+
5
4
,
−
1
2
,
−
3
+
5
2
,
±
1
+
5
4
)
,
{\displaystyle \left(\pm {\frac {3+{\sqrt {5}}}{4}},\,-{\frac {1}{2}},\,-{\frac {3+{\sqrt {5}}}{2}},\,\pm {\frac {1+{\sqrt {5}}}{4}}\right),}
(
±
3
+
5
4
,
1
2
,
3
+
5
2
,
1
+
5
4
)
,
{\displaystyle \left(\pm {\frac {3+{\sqrt {5}}}{4}},\,{\frac {1}{2}},\,{\frac {3+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{4}}\right),}
(
−
3
+
5
4
,
±
1
2
,
3
+
5
2
,
−
1
+
5
4
)
,
{\displaystyle \left(-{\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}},\,{\frac {3+{\sqrt {5}}}{2}},\,-{\frac {1+{\sqrt {5}}}{4}}\right),}
(
−
3
+
5
4
,
1
2
,
−
3
+
5
2
,
−
1
+
5
4
)
,
{\displaystyle \left(-{\frac {3+{\sqrt {5}}}{4}},\,{\frac {1}{2}},\,-{\frac {3+{\sqrt {5}}}{2}},\,-{\frac {1+{\sqrt {5}}}{4}}\right),}
(
3
+
5
4
,
−
1
2
,
3
+
5
2
,
1
+
5
4
)
,
{\displaystyle \left({\frac {3+{\sqrt {5}}}{4}},\,-{\frac {1}{2}},\,{\frac {3+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{4}}\right),}
(
3
+
5
4
,
1
2
,
−
3
+
5
2
,
1
+
5
4
)
,
{\displaystyle \left({\frac {3+{\sqrt {5}}}{4}},\,{\frac {1}{2}},\,-{\frac {3+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{4}}\right),}
(
3
+
5
4
,
1
2
,
3
+
5
2
,
−
1
+
5
4
)
,
{\displaystyle \left({\frac {3+{\sqrt {5}}}{4}},\,{\frac {1}{2}},\,{\frac {3+{\sqrt {5}}}{2}},\,-{\frac {1+{\sqrt {5}}}{4}}\right),}
(
±
3
+
5
4
,
−
1
+
5
4
,
1
2
,
3
+
5
2
)
,
{\displaystyle \left(\pm {\frac {3+{\sqrt {5}}}{4}},\,-{\frac {1+{\sqrt {5}}}{4}},\,{\frac {1}{2}},\,{\frac {3+{\sqrt {5}}}{2}}\right),}
(
−
3
+
5
4
,
−
1
+
5
4
,
±
1
2
,
−
3
+
5
2
)
,
{\displaystyle \left(-{\frac {3+{\sqrt {5}}}{4}},\,-{\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}},\,-{\frac {3+{\sqrt {5}}}{2}}\right),}
(
−
3
+
5
4
,
1
+
5
4
,
−
1
2
,
±
3
+
5
2
)
,
{\displaystyle \left(-{\frac {3+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{4}},\,-{\frac {1}{2}},\,\pm {\frac {3+{\sqrt {5}}}{2}}\right),}
(
−
3
+
5
4
,
1
+
5
4
,
1
2
,
−
3
+
5
2
)
,
{\displaystyle \left(-{\frac {3+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{4}},\,{\frac {1}{2}},\,-{\frac {3+{\sqrt {5}}}{2}}\right),}
(
3
+
5
4
,
±
1
+
5
4
,
−
1
2
,
3
+
5
2
)
,
{\displaystyle \left({\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {1+{\sqrt {5}}}{4}},\,-{\frac {1}{2}},\,{\frac {3+{\sqrt {5}}}{2}}\right),}
(
3
+
5
4
,
−
1
+
5
4
,
1
2
,
−
3
+
5
2
)
,
{\displaystyle \left({\frac {3+{\sqrt {5}}}{4}},\,-{\frac {1+{\sqrt {5}}}{4}},\,{\frac {1}{2}},\,-{\frac {3+{\sqrt {5}}}{2}}\right),}
(
3
+
5
4
,
1
+
5
4
,
−
1
2
,
−
3
+
5
2
)
,
{\displaystyle \left({\frac {3+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{4}},\,-{\frac {1}{2}},\,-{\frac {3+{\sqrt {5}}}{2}}\right),}
(
3
+
5
4
,
1
+
5
4
,
1
2
,
3
+
5
2
)
,
{\displaystyle \left({\frac {3+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{4}},\,{\frac {1}{2}},\,{\frac {3+{\sqrt {5}}}{2}}\right),}
(
±
3
+
5
4
,
±
3
+
5
2
,
±
1
+
5
4
,
±
1
2
)
,
{\displaystyle \left(\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {3+{\sqrt {5}}}{2}},\,\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}}\right),}
(
±
3
+
5
2
,
−
1
2
,
−
1
+
5
4
,
±
3
+
5
4
)
,
{\displaystyle \left(\pm {\frac {3+{\sqrt {5}}}{2}},\,-{\frac {1}{2}},\,-{\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {3+{\sqrt {5}}}{4}}\right),}
(
±
3
+
5
2
,
1
2
,
1
+
5
4
,
−
3
+
5
4
)
,
{\displaystyle \left(\pm {\frac {3+{\sqrt {5}}}{2}},\,{\frac {1}{2}},\,{\frac {1+{\sqrt {5}}}{4}},\,-{\frac {3+{\sqrt {5}}}{4}}\right),}
(
−
3
+
5
2
,
±
1
2
,
1
+
5
4
,
3
+
5
4
)
,
{\displaystyle \left(-{\frac {3+{\sqrt {5}}}{2}},\,\pm {\frac {1}{2}},\,{\frac {1+{\sqrt {5}}}{4}},\,{\frac {3+{\sqrt {5}}}{4}}\right),}
(
−
3
+
5
2
,
1
2
,
−
1
+
5
4
,
3
+
5
4
)
,
{\displaystyle \left(-{\frac {3+{\sqrt {5}}}{2}},\,{\frac {1}{2}},\,-{\frac {1+{\sqrt {5}}}{4}},\,{\frac {3+{\sqrt {5}}}{4}}\right),}
(
3
+
5
2
,
−
1
2
,
1
+
5
4
,
−
3
+
5
4
)
,
{\displaystyle \left({\frac {3+{\sqrt {5}}}{2}},\,-{\frac {1}{2}},\,{\frac {1+{\sqrt {5}}}{4}},\,-{\frac {3+{\sqrt {5}}}{4}}\right),}
(
3
+
5
2
,
1
2
,
−
1
+
5
4
,
−
3
+
5
4
)
,
{\displaystyle \left({\frac {3+{\sqrt {5}}}{2}},\,{\frac {1}{2}},\,-{\frac {1+{\sqrt {5}}}{4}},\,-{\frac {3+{\sqrt {5}}}{4}}\right),}
(
3
+
5
2
,
1
2
,
1
+
5
4
,
3
+
5
4
)
,
{\displaystyle \left({\frac {3+{\sqrt {5}}}{2}},\,{\frac {1}{2}},\,{\frac {1+{\sqrt {5}}}{4}},\,{\frac {3+{\sqrt {5}}}{4}}\right),}
(
±
3
+
5
2
,
−
1
+
5
4
,
−
3
+
5
4
,
±
1
2
)
,
{\displaystyle \left(\pm {\frac {3+{\sqrt {5}}}{2}},\,-{\frac {1+{\sqrt {5}}}{4}},\,-{\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}}\right),}
(
±
3
+
5
2
,
1
+
5
4
,
3
+
5
4
,
1
2
)
,
{\displaystyle \left(\pm {\frac {3+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{4}},\,{\frac {3+{\sqrt {5}}}{4}},\,{\frac {1}{2}}\right),}
(
−
3
+
5
2
,
±
1
+
5
4
,
3
+
5
4
,
−
1
2
)
,
{\displaystyle \left(-{\frac {3+{\sqrt {5}}}{2}},\,\pm {\frac {1+{\sqrt {5}}}{4}},\,{\frac {3+{\sqrt {5}}}{4}},\,-{\frac {1}{2}}\right),}
(
−
3
+
5
2
,
1
+
5
4
,
−
3
+
5
4
,
−
1
2
)
,
{\displaystyle \left(-{\frac {3+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{4}},\,-{\frac {3+{\sqrt {5}}}{4}},\,-{\frac {1}{2}}\right),}
(
3
+
5
2
,
−
1
+
5
4
,
3
+
5
4
,
1
2
)
,
{\displaystyle \left({\frac {3+{\sqrt {5}}}{2}},\,-{\frac {1+{\sqrt {5}}}{4}},\,{\frac {3+{\sqrt {5}}}{4}},\,{\frac {1}{2}}\right),}
(
3
+
5
2
,
1
+
5
4
,
−
3
+
5
4
,
1
2
)
,
{\displaystyle \left({\frac {3+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{4}},\,-{\frac {3+{\sqrt {5}}}{4}},\,{\frac {1}{2}}\right),}
(
3
+
5
2
,
1
+
5
4
,
3
+
5
4
,
−
1
2
)
,
{\displaystyle \left({\frac {3+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{4}},\,{\frac {3+{\sqrt {5}}}{4}},\,-{\frac {1}{2}}\right),}
(
±
3
+
5
2
,
±
3
+
5
4
,
±
1
2
,
±
1
+
5
4
)
,
{\displaystyle \left(\pm {\frac {3+{\sqrt {5}}}{2}},\,\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {5}}}{4}}\right),}
(
±
1
+
5
4
)
,
±
3
+
5
4
,
±
1
+
5
2
,
±
2
+
5
2
)
,
{\displaystyle \left(\pm {\frac {1+{\sqrt {5}}}{4}}),\,\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {2+{\sqrt {5}}}{2}}\right),}
(
±
1
+
5
4
)
,
−
1
+
5
2
,
2
+
5
2
,
−
3
+
5
4
)
,
{\displaystyle \left(\pm {\frac {1+{\sqrt {5}}}{4}}),\,-{\frac {1+{\sqrt {5}}}{2}},\,{\frac {2+{\sqrt {5}}}{2}},\,-{\frac {3+{\sqrt {5}}}{4}}\right),}
(
−
1
+
5
4
)
,
−
1
+
5
2
,
±
2
+
5
2
,
3
+
5
4
)
,
{\displaystyle \left(-{\frac {1+{\sqrt {5}}}{4}}),\,-{\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {2+{\sqrt {5}}}{2}},\,{\frac {3+{\sqrt {5}}}{4}}\right),}
(
−
1
+
5
4
)
,
1
+
5
2
,
−
2
+
5
2
,
±
3
+
5
4
)
,
{\displaystyle \left(-{\frac {1+{\sqrt {5}}}{4}}),\,{\frac {1+{\sqrt {5}}}{2}},\,-{\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {3+{\sqrt {5}}}{4}}\right),}
(
−
1
+
5
4
)
,
1
+
5
2
,
2
+
5
2
,
3
+
5
4
)
,
{\displaystyle \left(-{\frac {1+{\sqrt {5}}}{4}}),\,{\frac {1+{\sqrt {5}}}{2}},\,{\frac {2+{\sqrt {5}}}{2}},\,{\frac {3+{\sqrt {5}}}{4}}\right),}
(
1
+
5
4
)
,
±
1
+
5
2
,
−
2
+
5
2
,
−
3
+
5
4
)
,
{\displaystyle \left({\frac {1+{\sqrt {5}}}{4}}),\,\pm {\frac {1+{\sqrt {5}}}{2}},\,-{\frac {2+{\sqrt {5}}}{2}},\,-{\frac {3+{\sqrt {5}}}{4}}\right),}
(
1
+
5
4
)
,
−
1
+
5
2
,
2
+
5
2
,
3
+
5
4
)
,
{\displaystyle \left({\frac {1+{\sqrt {5}}}{4}}),\,-{\frac {1+{\sqrt {5}}}{2}},\,{\frac {2+{\sqrt {5}}}{2}},\,{\frac {3+{\sqrt {5}}}{4}}\right),}
(
1
+
5
4
)
,
1
+
5
2
,
−
2
+
5
2
,
3
+
5
4
)
,
{\displaystyle \left({\frac {1+{\sqrt {5}}}{4}}),\,{\frac {1+{\sqrt {5}}}{2}},\,-{\frac {2+{\sqrt {5}}}{2}},\,{\frac {3+{\sqrt {5}}}{4}}\right),}
(
1
+
5
4
)
,
1
+
5
2
,
2
+
5
2
,
−
3
+
5
4
)
,
{\displaystyle \left({\frac {1+{\sqrt {5}}}{4}}),\,{\frac {1+{\sqrt {5}}}{2}},\,{\frac {2+{\sqrt {5}}}{2}},\,-{\frac {3+{\sqrt {5}}}{4}}\right),}
(
±
1
+
5
4
)
,
−
2
+
5
2
,
3
+
5
4
,
1
+
5
2
)
,
{\displaystyle \left(\pm {\frac {1+{\sqrt {5}}}{4}}),\,-{\frac {2+{\sqrt {5}}}{2}},\,{\frac {3+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{2}}\right),}
(
−
1
+
5
4
)
,
−
2
+
5
2
,
±
3
+
5
4
,
−
1
+
5
2
)
,
{\displaystyle \left(-{\frac {1+{\sqrt {5}}}{4}}),\,-{\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {3+{\sqrt {5}}}{4}},\,-{\frac {1+{\sqrt {5}}}{2}}\right),}
(
−
1
+
5
4
)
,
2
+
5
2
,
−
3
+
5
4
,
±
1
+
5
2
)
,
{\displaystyle \left(-{\frac {1+{\sqrt {5}}}{4}}),\,{\frac {2+{\sqrt {5}}}{2}},\,-{\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {1+{\sqrt {5}}}{2}}\right),}
(
−
1
+
5
4
)
,
2
+
5
2
,
3
+
5
4
,
−
1
+
5
2
)
,
{\displaystyle \left(-{\frac {1+{\sqrt {5}}}{4}}),\,{\frac {2+{\sqrt {5}}}{2}},\,{\frac {3+{\sqrt {5}}}{4}},\,-{\frac {1+{\sqrt {5}}}{2}}\right),}
(
1
+
5
4
)
,
±
2
+
5
2
,
−
3
+
5
4
,
1
+
5
2
)
,
{\displaystyle \left({\frac {1+{\sqrt {5}}}{4}}),\,\pm {\frac {2+{\sqrt {5}}}{2}},\,-{\frac {3+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{2}}\right),}
(
1
+
5
4
)
,
−
2
+
5
2
,
3
+
5
4
,
−
1
+
5
2
)
,
{\displaystyle \left({\frac {1+{\sqrt {5}}}{4}}),\,-{\frac {2+{\sqrt {5}}}{2}},\,{\frac {3+{\sqrt {5}}}{4}},\,-{\frac {1+{\sqrt {5}}}{2}}\right),}
(
1
+
5
4
)
,
2
+
5
2
,
−
3
+
5
4
,
−
1
+
5
2
)
,
{\displaystyle \left({\frac {1+{\sqrt {5}}}{4}}),\,{\frac {2+{\sqrt {5}}}{2}},\,-{\frac {3+{\sqrt {5}}}{4}},\,-{\frac {1+{\sqrt {5}}}{2}}\right),}
(
1
+
5
4
)
,
2
+
5
2
,
3
+
5
4
,
1
+
5
2
)
,
{\displaystyle \left({\frac {1+{\sqrt {5}}}{4}}),\,{\frac {2+{\sqrt {5}}}{2}},\,{\frac {3+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{2}}\right),}
(
±
3
+
5
4
,
±
1
+
5
4
,
±
2
+
5
2
,
±
1
+
5
2
)
,
{\displaystyle \left(\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {1+{\sqrt {5}}}{2}}\right),}
(
±
3
+
5
4
,
−
1
+
5
2
,
−
1
+
5
4
,
±
2
+
5
2
)
,
{\displaystyle \left(\pm {\frac {3+{\sqrt {5}}}{4}},\,-{\frac {1+{\sqrt {5}}}{2}},\,-{\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {2+{\sqrt {5}}}{2}}\right),}
(
±
3
+
5
4
,
1
+
5
2
,
1
+
5
4
,
−
2
+
5
2
)
,
{\displaystyle \left(\pm {\frac {3+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{4}},\,-{\frac {2+{\sqrt {5}}}{2}}\right),}
(
−
3
+
5
4
,
±
1
+
5
2
,
1
+
5
4
,
2
+
5
2
)
,
{\displaystyle \left(-{\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {1+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{4}},\,{\frac {2+{\sqrt {5}}}{2}}\right),}
(
−
3
+
5
4
,
1
+
5
2
,
−
1
+
5
4
,
2
+
5
2
)
,
{\displaystyle \left(-{\frac {3+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{2}},\,-{\frac {1+{\sqrt {5}}}{4}},\,{\frac {2+{\sqrt {5}}}{2}}\right),}
(
3
+
5
4
,
−
1
+
5
2
,
1
+
5
4
,
−
2
+
5
2
)
,
{\displaystyle \left({\frac {3+{\sqrt {5}}}{4}},\,-{\frac {1+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{4}},\,-{\frac {2+{\sqrt {5}}}{2}}\right),}
(
3
+
5
4
,
1
+
5
2
,
−
1
+
5
4
,
−
2
+
5
2
)
,
{\displaystyle \left({\frac {3+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{2}},\,-{\frac {1+{\sqrt {5}}}{4}},\,-{\frac {2+{\sqrt {5}}}{2}}\right),}
(
3
+
5
4
,
1
+
5
2
,
1
+
5
4
,
2
+
5
2
)
,
{\displaystyle \left({\frac {3+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{4}},\,{\frac {2+{\sqrt {5}}}{2}}\right),}
(
±
3
+
5
4
,
−
2
+
5
2
,
−
1
+
5
2
,
±
1
+
5
4
)
,
{\displaystyle \left(\pm {\frac {3+{\sqrt {5}}}{4}},\,-{\frac {2+{\sqrt {5}}}{2}},\,-{\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {1+{\sqrt {5}}}{4}}\right),}
(
±
3
+
5
4
,
2
+
5
2
,
1
+
5
2
,
1
+
5
4
)
,
{\displaystyle \left(\pm {\frac {3+{\sqrt {5}}}{4}},\,{\frac {2+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{4}}\right),}
(
−
3
+
5
4
,
±
2
+
5
2
,
1
+
5
2
,
−
1
+
5
4
)
,
{\displaystyle \left(-{\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {2+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{2}},\,-{\frac {1+{\sqrt {5}}}{4}}\right),}
(
−
3
+
5
4
,
2
+
5
2
,
−
1
+
5
2
,
−
1
+
5
4
)
,
{\displaystyle \left(-{\frac {3+{\sqrt {5}}}{4}},\,{\frac {2+{\sqrt {5}}}{2}},\,-{\frac {1+{\sqrt {5}}}{2}},\,-{\frac {1+{\sqrt {5}}}{4}}\right),}
(
3
+
5
4
,
−
2
+
5
2
,
1
+
5
2
,
1
+
5
4
)
,
{\displaystyle \left({\frac {3+{\sqrt {5}}}{4}},\,-{\frac {2+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{4}}\right),}
(
3
+
5
4
,
2
+
5
2
,
−
1
+
5
2
,
1
+
5
4
)
,
{\displaystyle \left({\frac {3+{\sqrt {5}}}{4}},\,{\frac {2+{\sqrt {5}}}{2}},\,-{\frac {1+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{4}}\right),}
(
3
+
5
4
,
2
+
5
2
,
1
+
5
2
,
−
1
+
5
4
)
,
{\displaystyle \left({\frac {3+{\sqrt {5}}}{4}},\,{\frac {2+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{2}},\,-{\frac {1+{\sqrt {5}}}{4}}\right),}
(
±
1
+
5
2
,
−
1
+
5
4
,
−
3
+
5
4
,
±
2
+
5
2
)
,
{\displaystyle \left(\pm {\frac {1+{\sqrt {5}}}{2}},\,-{\frac {1+{\sqrt {5}}}{4}},\,-{\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {2+{\sqrt {5}}}{2}}\right),}
(
±
1
+
5
2
,
1
+
5
4
,
3
+
5
4
,
2
+
5
2
)
,
{\displaystyle \left(\pm {\frac {1+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{4}},\,{\frac {3+{\sqrt {5}}}{4}},\,{\frac {2+{\sqrt {5}}}{2}}\right),}
(
−
1
+
5
2
,
±
1
+
5
4
,
3
+
5
4
,
−
2
+
5
2
)
,
{\displaystyle \left(-{\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {1+{\sqrt {5}}}{4}},\,{\frac {3+{\sqrt {5}}}{4}},\,-{\frac {2+{\sqrt {5}}}{2}}\right),}
(
−
1
+
5
2
,
1
+
5
4
,
−
3
+
5
4
,
−
2
+
5
2
)
,
{\displaystyle \left(-{\frac {1+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{4}},\,-{\frac {3+{\sqrt {5}}}{4}},\,-{\frac {2+{\sqrt {5}}}{2}}\right),}
(
1
+
5
2
,
−
1
+
5
4
,
3
+
5
4
,
2
+
5
2
)
,
{\displaystyle \left({\frac {1+{\sqrt {5}}}{2}},\,-{\frac {1+{\sqrt {5}}}{4}},\,{\frac {3+{\sqrt {5}}}{4}},\,{\frac {2+{\sqrt {5}}}{2}}\right),}
(
1
+
5
2
,
1
+
5
4
,
−
3
+
5
4
,
2
+
5
2
)
,
{\displaystyle \left({\frac {1+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{4}},\,-{\frac {3+{\sqrt {5}}}{4}},\,{\frac {2+{\sqrt {5}}}{2}}\right),}
(
1
+
5
2
,
1
+
5
4
,
3
+
5
4
,
−
2
+
5
2
)
,
{\displaystyle \left({\frac {1+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{4}},\,{\frac {3+{\sqrt {5}}}{4}},\,-{\frac {2+{\sqrt {5}}}{2}}\right),}
(
±
1
+
5
2
,
−
3
+
5
4
,
−
2
+
5
2
,
±
1
+
5
4
)
,
{\displaystyle \left(\pm {\frac {1+{\sqrt {5}}}{2}},\,-{\frac {3+{\sqrt {5}}}{4}},\,-{\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {1+{\sqrt {5}}}{4}}\right),}
(
±
1
+
5
2
,
3
+
5
4
,
2
+
5
2
,
−
1
+
5
4
)
,
{\displaystyle \left(\pm {\frac {1+{\sqrt {5}}}{2}},\,{\frac {3+{\sqrt {5}}}{4}},\,{\frac {2+{\sqrt {5}}}{2}},\,-{\frac {1+{\sqrt {5}}}{4}}\right),}
(
−
1
+
5
2
,
±
3
+
5
4
,
2
+
5
2
,
1
+
5
4
)
,
{\displaystyle \left(-{\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {3+{\sqrt {5}}}{4}},\,{\frac {2+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{4}}\right),}
(
−
1
+
5
2
,
3
+
5
4
,
−
2
+
5
2
,
1
+
5
4
)
,
{\displaystyle \left(-{\frac {1+{\sqrt {5}}}{2}},\,{\frac {3+{\sqrt {5}}}{4}},\,-{\frac {2+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{4}}\right),}
(
1
+
5
2
,
−
3
+
5
4
,
2
+
5
2
,
−
1
+
5
4
)
,
{\displaystyle \left({\frac {1+{\sqrt {5}}}{2}},\,-{\frac {3+{\sqrt {5}}}{4}},\,{\frac {2+{\sqrt {5}}}{2}},\,-{\frac {1+{\sqrt {5}}}{4}}\right),}
(
1
+
5
2
,
3
+
5
4
,
−
2
+
5
2
,
−
1
+
5
4
)
,
{\displaystyle \left({\frac {1+{\sqrt {5}}}{2}},\,{\frac {3+{\sqrt {5}}}{4}},\,-{\frac {2+{\sqrt {5}}}{2}},\,-{\frac {1+{\sqrt {5}}}{4}}\right),}
(
1
+
5
2
,
3
+
5
4
,
2
+
5
2
,
1
+
5
4
)
,
{\displaystyle \left({\frac {1+{\sqrt {5}}}{2}},\,{\frac {3+{\sqrt {5}}}{4}},\,{\frac {2+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{4}}\right),}
(
±
1
+
5
2
,
±
2
+
5
2
,
±
1
+
5
4
,
±
3
+
5
4
)
,
{\displaystyle \left(\pm {\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {3+{\sqrt {5}}}{4}}\right),}
(
±
2
+
5
2
,
−
1
+
5
4
,
1
+
5
2
,
3
+
5
4
)
,
{\displaystyle \left(\pm {\frac {2+{\sqrt {5}}}{2}},\,-{\frac {1+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{2}},\,{\frac {3+{\sqrt {5}}}{4}}\right),}
(
−
2
+
5
2
,
−
1
+
5
4
,
±
1
+
5
2
,
−
3
+
5
4
)
,
{\displaystyle \left(-{\frac {2+{\sqrt {5}}}{2}},\,-{\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {1+{\sqrt {5}}}{2}},\,-{\frac {3+{\sqrt {5}}}{4}}\right),}
(
−
2
+
5
2
,
1
+
5
4
,
−
1
+
5
2
,
±
3
+
5
4
)
,
{\displaystyle \left(-{\frac {2+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{4}},\,-{\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {3+{\sqrt {5}}}{4}}\right),}
(
−
2
+
5
2
,
1
+
5
4
,
1
+
5
2
,
−
3
+
5
4
)
,
{\displaystyle \left(-{\frac {2+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{2}},\,-{\frac {3+{\sqrt {5}}}{4}}\right),}
(
2
+
5
2
,
±
1
+
5
4
,
−
1
+
5
2
,
3
+
5
4
)
,
{\displaystyle \left({\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {1+{\sqrt {5}}}{4}},\,-{\frac {1+{\sqrt {5}}}{2}},\,{\frac {3+{\sqrt {5}}}{4}}\right),}
(
2
+
5
2
,
−
1
+
5
4
,
1
+
5
2
,
−
3
+
5
4
)
,
{\displaystyle \left({\frac {2+{\sqrt {5}}}{2}},\,-{\frac {1+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{2}},\,-{\frac {3+{\sqrt {5}}}{4}}\right),}
(
2
+
5
2
,
1
+
5
4
,
−
1
+
5
2
,
−
3
+
5
4
)
,
{\displaystyle \left({\frac {2+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{4}},\,-{\frac {1+{\sqrt {5}}}{2}},\,-{\frac {3+{\sqrt {5}}}{4}}\right),}
(
2
+
5
2
,
1
+
5
4
,
1
+
5
2
,
3
+
5
4
)
,
{\displaystyle \left({\frac {2+{\sqrt {5}}}{2}},\,{\frac {1+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{2}},\,{\frac {3+{\sqrt {5}}}{4}}\right),}
(
±
2
+
5
2
,
−
3
+
5
4
,
1
+
5
4
,
−
1
+
5
2
)
,
{\displaystyle \left(\pm {\frac {2+{\sqrt {5}}}{2}},\,-{\frac {3+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{4}},\,-{\frac {1+{\sqrt {5}}}{2}}\right),}
(
−
2
+
5
2
,
−
3
+
5
4
,
±
1
+
5
4
,
1
+
5
2
)
,
{\displaystyle \left(-{\frac {2+{\sqrt {5}}}{2}},\,-{\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {1+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{2}}\right),}
(
−
2
+
5
2
,
3
+
5
4
,
−
1
+
5
4
,
±
1
+
5
2
)
,
{\displaystyle \left(-{\frac {2+{\sqrt {5}}}{2}},\,{\frac {3+{\sqrt {5}}}{4}},\,-{\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {1+{\sqrt {5}}}{2}}\right),}
(
−
2
+
5
2
,
3
+
5
4
,
1
+
5
4
,
1
+
5
2
)
,
{\displaystyle \left(-{\frac {2+{\sqrt {5}}}{2}},\,{\frac {3+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{2}}\right),}
(
2
+
5
2
,
±
3
+
5
4
,
−
1
+
5
4
,
−
1
+
5
2
)
,
{\displaystyle \left({\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {3+{\sqrt {5}}}{4}},\,-{\frac {1+{\sqrt {5}}}{4}},\,-{\frac {1+{\sqrt {5}}}{2}}\right),}
(
2
+
5
2
,
−
3
+
5
4
,
1
+
5
4
,
1
+
5
2
)
,
{\displaystyle \left({\frac {2+{\sqrt {5}}}{2}},\,-{\frac {3+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{2}}\right),}
(
2
+
5
2
,
3
+
5
4
,
−
1
+
5
4
,
1
+
5
2
)
,
{\displaystyle \left({\frac {2+{\sqrt {5}}}{2}},\,{\frac {3+{\sqrt {5}}}{4}},\,-{\frac {1+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{2}}\right),}
(
2
+
5
2
,
3
+
5
4
,
1
+
5
4
,
−
1
+
5
2
)
,
{\displaystyle \left({\frac {2+{\sqrt {5}}}{2}},\,{\frac {3+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{4}},\,-{\frac {1+{\sqrt {5}}}{2}}\right),}
(
±
2
+
5
2
,
±
1
+
5
2
,
±
3
+
5
4
,
±
1
+
5
4
)
.
{\displaystyle \left(\pm {\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {1+{\sqrt {5}}}{4}}\right).}
These are derived by removing 120 vertices from the rectified hexacosichoron .
