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:
(
0
,
0
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±
1
+
5
2
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±
3
+
5
2
)
,
{\displaystyle \left(0,\,0,\,±\frac{1+\sqrt5}{2},\,±\frac{3+\sqrt5}{2}\right),}
(
0
,
0
,
±
3
+
5
2
,
±
1
+
5
2
)
,
{\displaystyle \left(0,\,0,\,±\frac{3+\sqrt5}{2},\,±\frac{1+\sqrt5}{2}\right),}
(
0
,
±
1
+
5
2
,
0
,
±
3
+
5
2
)
,
{\displaystyle \left(0,\,±\frac{1+\sqrt5}{2},\,0,\,±\frac{3+\sqrt5}{2}\right),}
(
0
,
−
1
+
5
2
,
−
3
+
5
2
,
0
)
,
{\displaystyle \left(0,\,-\frac{1+\sqrt5}{2},\,-\frac{3+\sqrt5}{2},\,0\right),}
(
0
,
1
+
5
2
,
3
+
5
2
,
0
)
,
{\displaystyle \left(0,\,\frac{1+\sqrt5}{2},\,\frac{3+\sqrt5}{2},\,0\right),}
(
0
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±
3
+
5
2
,
0
,
±
1
+
5
2
)
,
{\displaystyle \left(0,\,±\frac{3+\sqrt5}{2},\,0,\,±\frac{1+\sqrt5}{2}\right),}
(
0
,
−
3
+
5
2
,
1
+
5
2
,
0
)
,
{\displaystyle \left(0,\,-\frac{3+\sqrt5}{2},\,\frac{1+\sqrt5}{2},\,0\right),}
(
0
,
3
+
5
2
,
−
1
+
5
2
,
0
)
,
{\displaystyle \left(0,\,\frac{3+\sqrt5}{2},\,-\frac{1+\sqrt5}{2},\,0\right),}
(
−
1
+
5
2
,
0
,
0
,
3
+
5
2
)
,
{\displaystyle \left(-\frac{1+\sqrt5}{2},\,0,\,0,\,\frac{3+\sqrt5}{2}\right),}
(
1
+
5
2
,
0
,
0
,
−
3
+
5
2
)
,
{\displaystyle \left(\frac{1+\sqrt5}{2},\,0,\,0,\,-\frac{3+\sqrt5}{2}\right),}
(
±
1
+
5
2
,
0
,
±
3
+
5
2
,
0
)
,
{\displaystyle \left(±\frac{1+\sqrt5}{2},\,0,\,±\frac{3+\sqrt5}{2},\,0\right),}
(
±
1
+
5
2
,
±
3
+
5
2
,
0
,
0
)
,
{\displaystyle \left(±\frac{1+\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,0,\,0\right),}
(
−
3
+
5
2
,
0
,
0
,
−
1
+
5
2
)
,
{\displaystyle \left(-\frac{3+\sqrt5}{2},\,0,\,0,\,-\frac{1+\sqrt5}{2}\right),}
(
3
+
5
2
,
0
,
0
,
1
+
5
2
)
,
{\displaystyle \left(\frac{3+\sqrt5}{2},\,0,\,0,\,\frac{1+\sqrt5}{2}\right),}
(
±
3
+
5
2
,
0
,
±
1
+
5
2
,
0
)
,
{\displaystyle \left(±\frac{3+\sqrt5}{2},\,0,\,±\frac{1+\sqrt5}{2},\,0\right),}
(
±
3
+
5
2
,
±
1
+
5
2
,
0
,
0
)
,
{\displaystyle \left(±\frac{3+\sqrt5}{2},\,±\frac{1+\sqrt5}{2},\,0,\,0\right),}
(
0
,
−
1
2
,
−
1
+
5
4
,
±
5
+
3
5
4
)
,
{\displaystyle \left(0,\,-\frac12,\,-\frac{1+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4}\right),}
(
0
,
1
2
,
1
+
5
4
,
±
5
+
3
5
4
)
,
{\displaystyle \left(0,\,\frac12,\,\frac{1+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4}\right),}
(
0
,
±
1
+
5
4
,
±
5
+
3
5
4
,
±
1
2
)
,
{\displaystyle \left(0,\,±\frac{1+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac12\right),}
(
0
,
±
5
+
3
5
4
,
±
1
2
,
±
1
+
5
4
)
,
{\displaystyle \left(0,\,±\frac{5+3\sqrt5}{4},\,±\frac12,\,±\frac{1+\sqrt5}{4}\right),}
(
−
1
2
,
0
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±
5
+
3
5
4
,
1
+
5
4
)
,
{\displaystyle \left(-\frac12,\,0,\,±\frac{5+3\sqrt5}{4},\,\frac{1+\sqrt5}{4}\right),}
(
1
2
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0
,
±
5
+
3
5
4
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−
1
+
5
4
)
,
{\displaystyle \left(\frac12,\,0,\,±\frac{5+3\sqrt5}{4},\,-\frac{1+\sqrt5}{4}\right),}
(
±
1
2
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±
1
+
5
4
,
0
,
±
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3
5
4
)
,
{\displaystyle \left(±\frac12,\,±\frac{1+\sqrt5}{4},\,0,\,±\frac{5+3\sqrt5}{4}\right),}
(
±
1
2
,
±
5
+
3
5
4
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±
1
+
5
4
,
0
)
,
{\displaystyle \left(±\frac12,\,±\frac{5+3\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,0\right),}
(
±
1
+
5
4
)
,
0
,
±
1
2
,
±
5
+
3
5
4
)
,
{\displaystyle \left(±\frac{1+\sqrt5}{4}),\,0,\,±\frac12,\,±\frac{5+3\sqrt5}{4}\right),}
(
±
1
+
5
4
)
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±
1
2
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±
5
+
3
5
4
,
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,
{\displaystyle \left(±\frac{1+\sqrt5}{4}),\,±\frac12,\,±\frac{5+3\sqrt5}{4},\,0\right),}
(
−
1
+
5
4
)
,
±
5
+
3
5
4
,
0
,
−
1
2
)
,
{\displaystyle \left(-\frac{1+\sqrt5}{4}),\,±\frac{5+3\sqrt5}{4},\,0,\,-\frac12\right),}
(
1
+
5
4
)
,
±
5
+
3
5
4
,
0
,
1
2
)
,
{\displaystyle \left(\frac{1+\sqrt5}{4}),\,±\frac{5+3\sqrt5}{4},\,0,\,\frac12\right),}
(
±
5
+
3
5
4
,
0
,
±
1
+
5
4
,
±
1
2
)
,
{\displaystyle \left(±\frac{5+3\sqrt5}{4},\,0,\,±\frac{1+\sqrt5}{4},\,±\frac12\right),}
(
±
5
+
3
5
4
,
±
1
2
,
0
,
±
1
+
5
4
)
,
{\displaystyle \left(±\frac{5+3\sqrt5}{4},\,±\frac12,\,0,\,±\frac{1+\sqrt5}{4}\right),}
(
±
5
+
3
5
4
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−
1
+
5
4
,
1
2
,
0
)
,
{\displaystyle \left(±\frac{5+3\sqrt5}{4},\,-\frac{1+\sqrt5}{4},\,\frac12,\,0\right),}
(
±
5
+
3
5
4
,
1
+
5
4
,
−
1
2
,
0
)
,
{\displaystyle \left(±\frac{5+3\sqrt5}{4},\,\frac{1+\sqrt5}{4},\,-\frac12,\,0\right),}
(
0
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−
3
+
5
4
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−
2
+
5
2
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±
5
+
5
4
)
,
{\displaystyle \left(0,\,-\frac{3+\sqrt5}{4},\,-\frac{2+\sqrt5}{2},\,±\frac{5+\sqrt5}{4}\right),}
(
0
,
3
+
5
4
,
2
+
5
2
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±
5
+
5
4
)
,
{\displaystyle \left(0,\,\frac{3+\sqrt5}{4},\,\frac{2+\sqrt5}{2},\,±\frac{5+\sqrt5}{4}\right),}
(
0
,
±
5
+
5
4
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±
3
+
5
4
,
±
2
+
5
2
)
,
{\displaystyle \left(0,\,±\frac{5+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{2+\sqrt5}{2}\right),}
(
0
,
±
2
+
5
2
,
±
5
+
5
4
,
±
3
+
5
4
)
,
{\displaystyle \left(0,\,±\frac{2+\sqrt5}{2},\,±\frac{5+\sqrt5}{4},\,±\frac{3+\sqrt5}{4}\right),}
(
−
3
+
5
4
,
0
,
±
5
+
5
4
,
2
+
5
2
)
,
{\displaystyle \left(-\frac{3+\sqrt5}{4},\,0,\,±\frac{5+\sqrt5}{4},\,\frac{2+\sqrt5}{2}\right),}
(
3
+
5
4
,
0
,
±
5
+
5
4
,
−
2
+
5
2
)
,
{\displaystyle \left(\frac{3+\sqrt5}{4},\,0,\,±\frac{5+\sqrt5}{4},\,-\frac{2+\sqrt5}{2}\right),}
(
±
3
+
5
4
,
±
5
+
5
4
,
±
2
+
5
2
,
0
)
,
{\displaystyle \left(±\frac{3+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{2+\sqrt5}{2},\,0\right),}
(
±
3
+
5
4
,
±
2
+
5
2
,
0
,
±
5
+
5
4
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,
{\displaystyle \left(±\frac{3+\sqrt5}{4},\,±\frac{2+\sqrt5}{2},\,0,\,±\frac{5+\sqrt5}{4}\right),}
(
±
5
+
5
4
,
0
,
±
2
+
5
2
,
±
3
+
5
4
)
,
{\displaystyle \left(±\frac{5+\sqrt5}{4},\,0,\,±\frac{2+\sqrt5}{2},\,±\frac{3+\sqrt5}{4}\right),}
(
±
5
+
5
4
,
±
3
+
5
4
,
0
,
±
2
+
5
2
)
,
{\displaystyle \left(±\frac{5+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,0,\,±\frac{2+\sqrt5}{2}\right),}
(
±
5
+
5
4
,
−
2
+
5
2
,
3
+
5
4
,
0
)
,
{\displaystyle \left(±\frac{5+\sqrt5}{4},\,-\frac{2+\sqrt5}{2},\,\frac{3+\sqrt5}{4},\,0\right),}
(
±
5
+
5
4
,
2
+
5
2
,
−
3
+
5
4
,
0
)
,
{\displaystyle \left(±\frac{5+\sqrt5}{4},\,\frac{2+\sqrt5}{2},\,-\frac{3+\sqrt5}{4},\,0\right),}
(
±
2
+
5
2
,
0
,
±
3
+
5
4
,
±
5
+
5
4
)
,
{\displaystyle \left(±\frac{2+\sqrt5}{2},\,0,\,±\frac{3+\sqrt5}{4},\,±\frac{5+\sqrt5}{4}\right),}
(
±
2
+
5
2
,
±
3
+
5
4
,
±
5
+
5
4
,
0
)
,
{\displaystyle \left(±\frac{2+\sqrt5}{2},\,±\frac{3+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,0\right),}
(
−
2
+
5
2
,
±
5
+
5
4
,
0
,
−
3
+
5
4
)
,
{\displaystyle \left(-\frac{2+\sqrt5}{2},\,±\frac{5+\sqrt5}{4},\,0,\,-\frac{3+\sqrt5}{4}\right),}
(
2
+
5
2
,
±
5
+
5
4
,
0
,
3
+
5
4
)
,
{\displaystyle \left(\frac{2+\sqrt5}{2},\,±\frac{5+\sqrt5}{4},\,0,\,\frac{3+\sqrt5}{4}\right),}
(
−
1
2
,
−
1
2
,
±
2
+
5
2
,
−
2
+
5
2
)
,
{\displaystyle \left(-\frac12,\,-\frac12,\,±\frac{2+\sqrt5}{2},\,-\frac{2+\sqrt5}{2}\right),}
(
−
1
2
,
1
2
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−
2
+
5
2
,
±
2
+
5
2
)
,
{\displaystyle \left(-\frac12,\,\frac12,\,-\frac{2+\sqrt5}{2},\,±\frac{2+\sqrt5}{2}\right),}
(
−
1
2
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1
2
,
2
+
5
2
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−
2
+
5
2
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,
{\displaystyle \left(-\frac12,\,\frac12,\,\frac{2+\sqrt5}{2},\,-\frac{2+\sqrt5}{2}\right),}
(
1
2
,
±
1
2
,
−
2
+
5
2
,
2
+
5
2
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,
{\displaystyle \left(\frac12,\,±\frac12,\,-\frac{2+\sqrt5}{2},\,\frac{2+\sqrt5}{2}\right),}
(
1
2
,
−
1
2
,
2
+
5
2
,
−
2
+
5
2
)
,
{\displaystyle \left(\frac12,\,-\frac12,\,\frac{2+\sqrt5}{2},\,-\frac{2+\sqrt5}{2}\right),}
(
1
2
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1
2
,
−
2
+
5
2
,
−
2
+
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,
{\displaystyle \left(\frac12,\,\frac12,\,-\frac{2+\sqrt5}{2},\,-\frac{2+\sqrt5}{2}\right),}
(
1
2
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2
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2
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2
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{\displaystyle \left(\frac12,\,\frac12,\,\frac{2+\sqrt5}{2},\,\frac{2+\sqrt5}{2}\right),}
(
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2
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{\displaystyle \left(±\frac12,\,-\frac{2+\sqrt5}{2},\,-\frac12,\,±\frac{2+\sqrt5}{2}\right),}
(
±
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2
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{\displaystyle \left(±\frac12,\,\frac{2+\sqrt5}{2},\,\frac12,\,\frac{2+\sqrt5}{2}\right),}
(
−
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2
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2
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1
2
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−
2
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{\displaystyle \left(-\frac12,\,±\frac{2+\sqrt5}{2},\,\frac12,\,-\frac{2+\sqrt5}{2}\right),}
(
−
1
2
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2
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5
2
,
−
1
2
,
−
2
+
5
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,
{\displaystyle \left(-\frac12,\,\frac{2+\sqrt5}{2},\,-\frac12,\,-\frac{2+\sqrt5}{2}\right),}
(
1
2
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−
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5
2
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1
2
,
2
+
5
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,
{\displaystyle \left(\frac12,\,-\frac{2+\sqrt5}{2},\,\frac12,\,\frac{2+\sqrt5}{2}\right),}
(
1
2
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2
+
5
2
,
−
1
2
,
2
+
5
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,
{\displaystyle \left(\frac12,\,\frac{2+\sqrt5}{2},\,-\frac12,\,\frac{2+\sqrt5}{2}\right),}
(
1
2
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2
+
5
2
,
1
2
,
−
2
+
5
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,
{\displaystyle \left(\frac12,\,\frac{2+\sqrt5}{2},\,\frac12,\,-\frac{2+\sqrt5}{2}\right),}
(
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1
2
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2
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±
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+
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,
{\displaystyle \left(±\frac12,\,±\frac{2+\sqrt5}{2},\,±\frac{2+\sqrt5}{2},\,±\frac12\right),}
(
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2
+
5
2
,
±
1
2
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±
1
2
,
±
2
+
5
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)
,
{\displaystyle \left(±\frac{2+\sqrt5}{2},\,±\frac12,\,±\frac12,\,±\frac{2+\sqrt5}{2}\right),}
(
±
2
+
5
2
,
−
1
2
,
2
+
5
2
,
−
1
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)
,
{\displaystyle \left(±\frac{2+\sqrt5}{2},\,-\frac12,\,\frac{2+\sqrt5}{2},\,-\frac12\right),}
(
−
2
+
5
2
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−
1
2
,
±
2
+
5
2
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{\displaystyle \left(-\frac{2+\sqrt5}{2},\,-\frac12,\,±\frac{2+\sqrt5}{2},\,\frac12\right),}
(
−
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5
2
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1
2
,
−
2
+
5
2
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±
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{\displaystyle \left(-\frac{2+\sqrt5}{2},\,\frac12,\,-\frac{2+\sqrt5}{2},\,±\frac12\right),}
(
−
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+
5
2
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1
2
,
2
+
5
2
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1
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{\displaystyle \left(-\frac{2+\sqrt5}{2},\,\frac12,\,\frac{2+\sqrt5}{2},\,\frac12\right),}
(
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2
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±
1
2
,
−
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+
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2
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−
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,
{\displaystyle \left(\frac{2+\sqrt5}{2},\,±\frac12,\,-\frac{2+\sqrt5}{2},\,-\frac12\right),}
(
2
+
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2
,
−
1
2
,
2
+
5
2
,
1
2
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,
{\displaystyle \left(\frac{2+\sqrt5}{2},\,-\frac12,\,\frac{2+\sqrt5}{2},\,\frac12\right),}
(
2
+
5
2
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1
2
,
−
2
+
5
2
,
1
2
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,
{\displaystyle \left(\frac{2+\sqrt5}{2},\,\frac12,\,-\frac{2+\sqrt5}{2},\,\frac12\right),}
(
2
+
5
2
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1
2
,
2
+
5
2
,
−
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2
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,
{\displaystyle \left(\frac{2+\sqrt5}{2},\,\frac12,\,\frac{2+\sqrt5}{2},\,-\frac12\right),}
(
±
2
+
5
2
,
−
2
+
5
2
,
−
1
2
,
±
1
2
)
,
{\displaystyle \left(±\frac{2+\sqrt5}{2},\,-\frac{2+\sqrt5}{2},\,-\frac12,\,±\frac12\right),}
(
±
2
+
5
2
,
2
+
5
2
,
1
2
,
−
1
2
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,
{\displaystyle \left(±\frac{2+\sqrt5}{2},\,\frac{2+\sqrt5}{2},\,\frac12,\,-\frac12\right),}
(
−
2
+
5
2
,
±
2
+
5
2
,
1
2
,
1
2
)
,
{\displaystyle \left(-\frac{2+\sqrt5}{2},\,±\frac{2+\sqrt5}{2},\,\frac12,\,\frac12\right),}
(
−
2
+
5
2
,
2
+
5
2
,
−
1
2
,
1
2
)
,
{\displaystyle \left(-\frac{2+\sqrt5}{2},\,\frac{2+\sqrt5}{2},\,-\frac12,\,\frac12\right),}
(
2
+
5
2
,
−
2
+
5
2
,
1
2
,
−
1
2
)
,
{\displaystyle \left(\frac{2+\sqrt5}{2},\,-\frac{2+\sqrt5}{2},\,\frac12,\,-\frac12\right),}
(
2
+
5
2
,
2
+
5
2
,
−
1
2
,
−
1
2
)
,
{\displaystyle \left(\frac{2+\sqrt5}{2},\,\frac{2+\sqrt5}{2},\,-\frac12,\,-\frac12\right),}
(
2
+
5
2
,
2
+
5
2
,
1
2
,
1
2
)
,
{\displaystyle \left(\frac{2+\sqrt5}{2},\,\frac{2+\sqrt5}{2},\,\frac12,\,\frac12\right),}
(
±
1
2
,
±
1
+
5
4
,
±
3
+
5
2
,
±
3
+
5
4
)
,
{\displaystyle \left(±\frac12,\,±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac{3+\sqrt5}{4}\right),}
(
±
1
2
,
−
3
+
5
4
,
1
+
5
4
,
−
3
+
5
2
)
,
{\displaystyle \left(±\frac12,\,-\frac{3+\sqrt5}{4},\,\frac{1+\sqrt5}{4},\,-\frac{3+\sqrt5}{2}\right),}
(
−
1
2
,
−
3
+
5
4
,
±
1
+
5
4
,
3
+
5
2
)
,
{\displaystyle \left(-\frac12,\,-\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,\frac{3+\sqrt5}{2}\right),}
(
−
1
2
,
3
+
5
4
,
−
1
+
5
4
,
±
3
+
5
2
)
,
{\displaystyle \left(-\frac12,\,\frac{3+\sqrt5}{4},\,-\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{2}\right),}
(
−
1
2
,
3
+
5
4
,
1
+
5
4
,
3
+
5
2
)
,
{\displaystyle \left(-\frac12,\,\frac{3+\sqrt5}{4},\,\frac{1+\sqrt5}{4},\,\frac{3+\sqrt5}{2}\right),}
(
1
2
,
±
3
+
5
4
,
−
1
+
5
4
,
−
3
+
5
2
)
,
{\displaystyle \left(\frac12,\,±\frac{3+\sqrt5}{4},\,-\frac{1+\sqrt5}{4},\,-\frac{3+\sqrt5}{2}\right),}
(
1
2
,
−
3
+
5
4
,
1
+
5
4
,
3
+
5
2
)
,
{\displaystyle \left(\frac12,\,-\frac{3+\sqrt5}{4},\,\frac{1+\sqrt5}{4},\,\frac{3+\sqrt5}{2}\right),}
(
1
2
,
3
+
5
4
,
−
1
+
5
4
,
3
+
5
2
)
,
{\displaystyle \left(\frac12,\,\frac{3+\sqrt5}{4},\,-\frac{1+\sqrt5}{4},\,\frac{3+\sqrt5}{2}\right),}
(
1
2
,
3
+
5
4
,
1
+
5
4
,
−
3
+
5
2
)
,
{\displaystyle \left(\frac12,\,\frac{3+\sqrt5}{4},\,\frac{1+\sqrt5}{4},\,-\frac{3+\sqrt5}{2}\right),}
(
±
1
2
,
−
3
+
5
2
,
−
3
+
5
4
,
±
1
+
5
4
)
,
{\displaystyle \left(±\frac12,\,-\frac{3+\sqrt5}{2},\,-\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{4}\right),}
(
±
1
2
,
3
+
5
2
,
3
+
5
4
,
−
1
+
5
4
)
,
{\displaystyle \left(±\frac12,\,\frac{3+\sqrt5}{2},\,\frac{3+\sqrt5}{4},\,-\frac{1+\sqrt5}{4}\right),}
(
−
1
2
,
±
3
+
5
2
,
3
+
5
4
,
1
+
5
4
)
,
{\displaystyle \left(-\frac12,\,±\frac{3+\sqrt5}{2},\,\frac{3+\sqrt5}{4},\,\frac{1+\sqrt5}{4}\right),}
(
−
1
2
,
3
+
5
2
,
−
3
+
5
4
,
1
+
5
4
)
,
{\displaystyle \left(-\frac12,\,\frac{3+\sqrt5}{2},\,-\frac{3+\sqrt5}{4},\,\frac{1+\sqrt5}{4}\right),}
(
1
2
,
−
3
+
5
2
,
3
+
5
4
,
−
1
+
5
4
)
,
{\displaystyle \left(\frac12,\,-\frac{3+\sqrt5}{2},\,\frac{3+\sqrt5}{4},\,-\frac{1+\sqrt5}{4}\right),}
(
1
2
,
3
+
5
2
,
−
3
+
5
4
,
−
1
+
5
4
)
,
{\displaystyle \left(\frac12,\,\frac{3+\sqrt5}{2},\,-\frac{3+\sqrt5}{4},\,-\frac{1+\sqrt5}{4}\right),}
(
1
2
,
3
+
5
2
,
3
+
5
4
,
1
+
5
4
)
,
{\displaystyle \left(\frac12,\,\frac{3+\sqrt5}{2},\,\frac{3+\sqrt5}{4},\,\frac{1+\sqrt5}{4}\right),}
(
±
1
+
5
4
)
,
±
1
2
,
±
3
+
5
4
,
±
3
+
5
2
)
,
{\displaystyle \left(±\frac{1+\sqrt5}{4}),\,±\frac12,\,±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{2}\right),}
(
±
1
+
5
4
)
,
−
3
+
5
4
,
3
+
5
2
,
1
2
)
,
{\displaystyle \left(±\frac{1+\sqrt5}{4}),\,-\frac{3+\sqrt5}{4},\,\frac{3+\sqrt5}{2},\,\frac12\right),}
(
−
1
+
5
4
)
,
−
3
+
5
4
,
±
3
+
5
2
,
−
1
2
)
,
{\displaystyle \left(-\frac{1+\sqrt5}{4}),\,-\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,-\frac12\right),}
(
−
1
+
5
4
)
,
3
+
5
4
,
−
3
+
5
2
,
±
1
2
)
,
{\displaystyle \left(-\frac{1+\sqrt5}{4}),\,\frac{3+\sqrt5}{4},\,-\frac{3+\sqrt5}{2},\,±\frac12\right),}
(
−
1
+
5
4
)
,
3
+
5
4
,
3
+
5
2
,
−
1
2
)
,
{\displaystyle \left(-\frac{1+\sqrt5}{4}),\,\frac{3+\sqrt5}{4},\,\frac{3+\sqrt5}{2},\,-\frac12\right),}
(
1
+
5
4
)
,
±
3
+
5
4
,
−
3
+
5
2
,
1
2
)
,
{\displaystyle \left(\frac{1+\sqrt5}{4}),\,±\frac{3+\sqrt5}{4},\,-\frac{3+\sqrt5}{2},\,\frac12\right),}
(
1
+
5
4
)
,
−
3
+
5
4
,
3
+
5
2
,
−
1
2
)
,
{\displaystyle \left(\frac{1+\sqrt5}{4}),\,-\frac{3+\sqrt5}{4},\,\frac{3+\sqrt5}{2},\,-\frac12\right),}
(
1
+
5
4
)
,
3
+
5
4
,
−
3
+
5
2
,
−
1
2
)
,
{\displaystyle \left(\frac{1+\sqrt5}{4}),\,\frac{3+\sqrt5}{4},\,-\frac{3+\sqrt5}{2},\,-\frac12\right),}
(
1
+
5
4
)
,
3
+
5
4
,
3
+
5
2
,
1
2
)
,
{\displaystyle \left(\frac{1+\sqrt5}{4}),\,\frac{3+\sqrt5}{4},\,\frac{3+\sqrt5}{2},\,\frac12\right),}
(
±
1
+
5
4
)
,
−
3
+
5
2
,
1
2
,
−
3
+
5
4
)
,
{\displaystyle \left(±\frac{1+\sqrt5}{4}),\,-\frac{3+\sqrt5}{2},\,\frac12,\,-\frac{3+\sqrt5}{4}\right),}
(
−
1
+
5
4
)
,
−
3
+
5
2
,
±
1
2
,
3
+
5
4
)
,
{\displaystyle \left(-\frac{1+\sqrt5}{4}),\,-\frac{3+\sqrt5}{2},\,±\frac12,\,\frac{3+\sqrt5}{4}\right),}
(
−
1
+
5
4
)
,
3
+
5
2
,
−
1
2
,
±
3
+
5
4
)
,
{\displaystyle \left(-\frac{1+\sqrt5}{4}),\,\frac{3+\sqrt5}{2},\,-\frac12,\,±\frac{3+\sqrt5}{4}\right),}
(
−
1
+
5
4
)
,
3
+
5
2
,
1
2
,
3
+
5
4
)
,
{\displaystyle \left(-\frac{1+\sqrt5}{4}),\,\frac{3+\sqrt5}{2},\,\frac12,\,\frac{3+\sqrt5}{4}\right),}
(
1
+
5
4
)
,
±
3
+
5
2
,
−
1
2
,
−
3
+
5
4
)
,
{\displaystyle \left(\frac{1+\sqrt5}{4}),\,±\frac{3+\sqrt5}{2},\,-\frac12,\,-\frac{3+\sqrt5}{4}\right),}
(
1
+
5
4
)
,
−
3
+
5
2
,
1
2
,
3
+
5
4
)
,
{\displaystyle \left(\frac{1+\sqrt5}{4}),\,-\frac{3+\sqrt5}{2},\,\frac12,\,\frac{3+\sqrt5}{4}\right),}
(
1
+
5
4
)
,
3
+
5
2
,
−
1
2
,
3
+
5
4
)
,
{\displaystyle \left(\frac{1+\sqrt5}{4}),\,\frac{3+\sqrt5}{2},\,-\frac12,\,\frac{3+\sqrt5}{4}\right),}
(
1
+
5
4
)
,
3
+
5
2
,
1
2
,
−
3
+
5
4
)
,
{\displaystyle \left(\frac{1+\sqrt5}{4}),\,\frac{3+\sqrt5}{2},\,\frac12,\,-\frac{3+\sqrt5}{4}\right),}
(
±
3
+
5
4
,
−
1
2
,
−
3
+
5
2
,
±
1
+
5
4
)
,
{\displaystyle \left(±\frac{3+\sqrt5}{4},\,-\frac12,\,-\frac{3+\sqrt5}{2},\,±\frac{1+\sqrt5}{4}\right),}
(
±
3
+
5
4
,
1
2
,
3
+
5
2
,
1
+
5
4
)
,
{\displaystyle \left(±\frac{3+\sqrt5}{4},\,\frac12,\,\frac{3+\sqrt5}{2},\,\frac{1+\sqrt5}{4}\right),}
(
−
3
+
5
4
,
±
1
2
,
3
+
5
2
,
−
1
+
5
4
)
,
{\displaystyle \left(-\frac{3+\sqrt5}{4},\,±\frac12,\,\frac{3+\sqrt5}{2},\,-\frac{1+\sqrt5}{4}\right),}
(
−
3
+
5
4
,
1
2
,
−
3
+
5
2
,
−
1
+
5
4
)
,
{\displaystyle \left(-\frac{3+\sqrt5}{4},\,\frac12,\,-\frac{3+\sqrt5}{2},\,-\frac{1+\sqrt5}{4}\right),}
(
3
+
5
4
,
−
1
2
,
3
+
5
2
,
1
+
5
4
)
,
{\displaystyle \left(\frac{3+\sqrt5}{4},\,-\frac12,\,\frac{3+\sqrt5}{2},\,\frac{1+\sqrt5}{4}\right),}
(
3
+
5
4
,
1
2
,
−
3
+
5
2
,
1
+
5
4
)
,
{\displaystyle \left(\frac{3+\sqrt5}{4},\,\frac12,\,-\frac{3+\sqrt5}{2},\,\frac{1+\sqrt5}{4}\right),}
(
3
+
5
4
,
1
2
,
3
+
5
2
,
−
1
+
5
4
)
,
{\displaystyle \left(\frac{3+\sqrt5}{4},\,\frac12,\,\frac{3+\sqrt5}{2},\,-\frac{1+\sqrt5}{4}\right),}
(
±
3
+
5
4
,
−
1
+
5
4
,
1
2
,
3
+
5
2
)
,
{\displaystyle \left(±\frac{3+\sqrt5}{4},\,-\frac{1+\sqrt5}{4},\,\frac12,\,\frac{3+\sqrt5}{2}\right),}
(
−
3
+
5
4
,
−
1
+
5
4
,
±
1
2
,
−
3
+
5
2
)
,
{\displaystyle \left(-\frac{3+\sqrt5}{4},\,-\frac{1+\sqrt5}{4},\,±\frac12,\,-\frac{3+\sqrt5}{2}\right),}
(
−
3
+
5
4
,
1
+
5
4
,
−
1
2
,
±
3
+
5
2
)
,
{\displaystyle \left(-\frac{3+\sqrt5}{4},\,\frac{1+\sqrt5}{4},\,-\frac12,\,±\frac{3+\sqrt5}{2}\right),}
(
−
3
+
5
4
,
1
+
5
4
,
1
2
,
−
3
+
5
2
)
,
{\displaystyle \left(-\frac{3+\sqrt5}{4},\,\frac{1+\sqrt5}{4},\,\frac12,\,-\frac{3+\sqrt5}{2}\right),}
(
3
+
5
4
,
±
1
+
5
4
,
−
1
2
,
3
+
5
2
)
,
{\displaystyle \left(\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,-\frac12,\,\frac{3+\sqrt5}{2}\right),}
(
3
+
5
4
,
−
1
+
5
4
,
1
2
,
−
3
+
5
2
)
,
{\displaystyle \left(\frac{3+\sqrt5}{4},\,-\frac{1+\sqrt5}{4},\,\frac12,\,-\frac{3+\sqrt5}{2}\right),}
(
3
+
5
4
,
1
+
5
4
,
−
1
2
,
−
3
+
5
2
)
,
{\displaystyle \left(\frac{3+\sqrt5}{4},\,\frac{1+\sqrt5}{4},\,-\frac12,\,-\frac{3+\sqrt5}{2}\right),}
(
3
+
5
4
,
1
+
5
4
,
1
2
,
3
+
5
2
)
,
{\displaystyle \left(\frac{3+\sqrt5}{4},\,\frac{1+\sqrt5}{4},\,\frac12,\,\frac{3+\sqrt5}{2}\right),}
(
±
3
+
5
4
,
±
3
+
5
2
,
±
1
+
5
4
,
±
1
2
)
,
{\displaystyle \left(±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac{1+\sqrt5}{4},\,±\frac12\right),}
(
±
3
+
5
2
,
−
1
2
,
−
1
+
5
4
,
±
3
+
5
4
)
,
{\displaystyle \left(±\frac{3+\sqrt5}{2},\,-\frac12,\,-\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{4}\right),}
(
±
3
+
5
2
,
1
2
,
1
+
5
4
,
−
3
+
5
4
)
,
{\displaystyle \left(±\frac{3+\sqrt5}{2},\,\frac12,\,\frac{1+\sqrt5}{4},\,-\frac{3+\sqrt5}{4}\right),}
(
−
3
+
5
2
,
±
1
2
,
1
+
5
4
,
3
+
5
4
)
,
{\displaystyle \left(-\frac{3+\sqrt5}{2},\,±\frac12,\,\frac{1+\sqrt5}{4},\,\frac{3+\sqrt5}{4}\right),}
(
−
3
+
5
2
,
1
2
,
−
1
+
5
4
,
3
+
5
4
)
,
{\displaystyle \left(-\frac{3+\sqrt5}{2},\,\frac12,\,-\frac{1+\sqrt5}{4},\,\frac{3+\sqrt5}{4}\right),}
(
3
+
5
2
,
−
1
2
,
1
+
5
4
,
−
3
+
5
4
)
,
{\displaystyle \left(\frac{3+\sqrt5}{2},\,-\frac12,\,\frac{1+\sqrt5}{4},\,-\frac{3+\sqrt5}{4}\right),}
(
3
+
5
2
,
1
2
,
−
1
+
5
4
,
−
3
+
5
4
)
,
{\displaystyle \left(\frac{3+\sqrt5}{2},\,\frac12,\,-\frac{1+\sqrt5}{4},\,-\frac{3+\sqrt5}{4}\right),}
(
3
+
5
2
,
1
2
,
1
+
5
4
,
3
+
5
4
)
,
{\displaystyle \left(\frac{3+\sqrt5}{2},\,\frac12,\,\frac{1+\sqrt5}{4},\,\frac{3+\sqrt5}{4}\right),}
(
±
3
+
5
2
,
−
1
+
5
4
,
−
3
+
5
4
,
±
1
2
)
,
{\displaystyle \left(±\frac{3+\sqrt5}{2},\,-\frac{1+\sqrt5}{4},\,-\frac{3+\sqrt5}{4},\,±\frac12\right),}
(
±
3
+
5
2
,
1
+
5
4
,
3
+
5
4
,
1
2
)
,
{\displaystyle \left(±\frac{3+\sqrt5}{2},\,\frac{1+\sqrt5}{4},\,\frac{3+\sqrt5}{4},\,\frac12\right),}
(
−
3
+
5
2
,
±
1
+
5
4
,
3
+
5
4
,
−
1
2
)
,
{\displaystyle \left(-\frac{3+\sqrt5}{2},\,±\frac{1+\sqrt5}{4},\,\frac{3+\sqrt5}{4},\,-\frac12\right),}
(
−
3
+
5
2
,
1
+
5
4
,
−
3
+
5
4
,
−
1
2
)
,
{\displaystyle \left(-\frac{3+\sqrt5}{2},\,\frac{1+\sqrt5}{4},\,-\frac{3+\sqrt5}{4},\,-\frac12\right),}
(
3
+
5
2
,
−
1
+
5
4
,
3
+
5
4
,
1
2
)
,
{\displaystyle \left(\frac{3+\sqrt5}{2},\,-\frac{1+\sqrt5}{4},\,\frac{3+\sqrt5}{4},\,\frac12\right),}
(
3
+
5
2
,
1
+
5
4
,
−
3
+
5
4
,
1
2
)
,
{\displaystyle \left(\frac{3+\sqrt5}{2},\,\frac{1+\sqrt5}{4},\,-\frac{3+\sqrt5}{4},\,\frac12\right),}
(
3
+
5
2
,
1
+
5
4
,
3
+
5
4
,
−
1
2
)
,
{\displaystyle \left(\frac{3+\sqrt5}{2},\,\frac{1+\sqrt5}{4},\,\frac{3+\sqrt5}{4},\,-\frac12\right),}
(
±
3
+
5
2
,
±
3
+
5
4
,
±
1
2
,
±
1
+
5
4
)
,
{\displaystyle \left(±\frac{3+\sqrt5}{2},\,±\frac{3+\sqrt5}{4},\,±\frac12,\,±\frac{1+\sqrt5}{4}\right),}
(
±
1
+
5
4
)
,
±
3
+
5
4
,
±
1
+
5
2
,
±
2
+
5
2
)
,
{\displaystyle \left(±\frac{1+\sqrt5}{4}),\,±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{2+\sqrt5}{2}\right),}
(
±
1
+
5
4
)
,
−
1
+
5
2
,
2
+
5
2
,
−
3
+
5
4
)
,
{\displaystyle \left(±\frac{1+\sqrt5}{4}),\,-\frac{1+\sqrt5}{2},\,\frac{2+\sqrt5}{2},\,-\frac{3+\sqrt5}{4}\right),}
(
−
1
+
5
4
)
,
−
1
+
5
2
,
±
2
+
5
2
,
3
+
5
4
)
,
{\displaystyle \left(-\frac{1+\sqrt5}{4}),\,-\frac{1+\sqrt5}{2},\,±\frac{2+\sqrt5}{2},\,\frac{3+\sqrt5}{4}\right),}
(
−
1
+
5
4
)
,
1
+
5
2
,
−
2
+
5
2
,
±
3
+
5
4
)
,
{\displaystyle \left(-\frac{1+\sqrt5}{4}),\,\frac{1+\sqrt5}{2},\,-\frac{2+\sqrt5}{2},\,±\frac{3+\sqrt5}{4}\right),}
(
−
1
+
5
4
)
,
1
+
5
2
,
2
+
5
2
,
3
+
5
4
)
,
{\displaystyle \left(-\frac{1+\sqrt5}{4}),\,\frac{1+\sqrt5}{2},\,\frac{2+\sqrt5}{2},\,\frac{3+\sqrt5}{4}\right),}
(
1
+
5
4
)
,
±
1
+
5
2
,
−
2
+
5
2
,
−
3
+
5
4
)
,
{\displaystyle \left(\frac{1+\sqrt5}{4}),\,±\frac{1+\sqrt5}{2},\,-\frac{2+\sqrt5}{2},\,-\frac{3+\sqrt5}{4}\right),}
(
1
+
5
4
)
,
−
1
+
5
2
,
2
+
5
2
,
3
+
5
4
)
,
{\displaystyle \left(\frac{1+\sqrt5}{4}),\,-\frac{1+\sqrt5}{2},\,\frac{2+\sqrt5}{2},\,\frac{3+\sqrt5}{4}\right),}
(
1
+
5
4
)
,
1
+
5
2
,
−
2
+
5
2
,
3
+
5
4
)
,
{\displaystyle \left(\frac{1+\sqrt5}{4}),\,\frac{1+\sqrt5}{2},\,-\frac{2+\sqrt5}{2},\,\frac{3+\sqrt5}{4}\right),}
(
1
+
5
4
)
,
1
+
5
2
,
2
+
5
2
,
−
3
+
5
4
)
,
{\displaystyle \left(\frac{1+\sqrt5}{4}),\,\frac{1+\sqrt5}{2},\,\frac{2+\sqrt5}{2},\,-\frac{3+\sqrt5}{4}\right),}
(
±
1
+
5
4
)
,
−
2
+
5
2
,
3
+
5
4
,
1
+
5
2
)
,
{\displaystyle \left(±\frac{1+\sqrt5}{4}),\,-\frac{2+\sqrt5}{2},\,\frac{3+\sqrt5}{4},\,\frac{1+\sqrt5}{2}\right),}
(
−
1
+
5
4
)
,
−
2
+
5
2
,
±
3
+
5
4
,
−
1
+
5
2
)
,
{\displaystyle \left(-\frac{1+\sqrt5}{4}),\,-\frac{2+\sqrt5}{2},\,±\frac{3+\sqrt5}{4},\,-\frac{1+\sqrt5}{2}\right),}
(
−
1
+
5
4
)
,
2
+
5
2
,
−
3
+
5
4
,
±
1
+
5
2
)
,
{\displaystyle \left(-\frac{1+\sqrt5}{4}),\,\frac{2+\sqrt5}{2},\,-\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{2}\right),}
(
−
1
+
5
4
)
,
2
+
5
2
,
3
+
5
4
,
−
1
+
5
2
)
,
{\displaystyle \left(-\frac{1+\sqrt5}{4}),\,\frac{2+\sqrt5}{2},\,\frac{3+\sqrt5}{4},\,-\frac{1+\sqrt5}{2}\right),}
(
1
+
5
4
)
,
±
2
+
5
2
,
−
3
+
5
4
,
1
+
5
2
)
,
{\displaystyle \left(\frac{1+\sqrt5}{4}),\,±\frac{2+\sqrt5}{2},\,-\frac{3+\sqrt5}{4},\,\frac{1+\sqrt5}{2}\right),}
(
1
+
5
4
)
,
−
2
+
5
2
,
3
+
5
4
,
−
1
+
5
2
)
,
{\displaystyle \left(\frac{1+\sqrt5}{4}),\,-\frac{2+\sqrt5}{2},\,\frac{3+\sqrt5}{4},\,-\frac{1+\sqrt5}{2}\right),}
(
1
+
5
4
)
,
2
+
5
2
,
−
3
+
5
4
,
−
1
+
5
2
)
,
{\displaystyle \left(\frac{1+\sqrt5}{4}),\,\frac{2+\sqrt5}{2},\,-\frac{3+\sqrt5}{4},\,-\frac{1+\sqrt5}{2}\right),}
(
1
+
5
4
)
,
2
+
5
2
,
3
+
5
4
,
1
+
5
2
)
,
{\displaystyle \left(\frac{1+\sqrt5}{4}),\,\frac{2+\sqrt5}{2},\,\frac{3+\sqrt5}{4},\,\frac{1+\sqrt5}{2}\right),}
(
±
3
+
5
4
,
±
1
+
5
4
,
±
2
+
5
2
,
±
1
+
5
2
)
,
{\displaystyle \left(±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{2+\sqrt5}{2},\,±\frac{1+\sqrt5}{2}\right),}
(
±
3
+
5
4
,
−
1
+
5
2
,
−
1
+
5
4
,
±
2
+
5
2
)
,
{\displaystyle \left(±\frac{3+\sqrt5}{4},\,-\frac{1+\sqrt5}{2},\,-\frac{1+\sqrt5}{4},\,±\frac{2+\sqrt5}{2}\right),}
(
±
3
+
5
4
,
1
+
5
2
,
1
+
5
4
,
−
2
+
5
2
)
,
{\displaystyle \left(±\frac{3+\sqrt5}{4},\,\frac{1+\sqrt5}{2},\,\frac{1+\sqrt5}{4},\,-\frac{2+\sqrt5}{2}\right),}
(
−
3
+
5
4
,
±
1
+
5
2
,
1
+
5
4
,
2
+
5
2
)
,
{\displaystyle \left(-\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,\frac{1+\sqrt5}{4},\,\frac{2+\sqrt5}{2}\right),}
(
−
3
+
5
4
,
1
+
5
2
,
−
1
+
5
4
,
2
+
5
2
)
,
{\displaystyle \left(-\frac{3+\sqrt5}{4},\,\frac{1+\sqrt5}{2},\,-\frac{1+\sqrt5}{4},\,\frac{2+\sqrt5}{2}\right),}
(
3
+
5
4
,
−
1
+
5
2
,
1
+
5
4
,
−
2
+
5
2
)
,
{\displaystyle \left(\frac{3+\sqrt5}{4},\,-\frac{1+\sqrt5}{2},\,\frac{1+\sqrt5}{4},\,-\frac{2+\sqrt5}{2}\right),}
(
3
+
5
4
,
1
+
5
2
,
−
1
+
5
4
,
−
2
+
5
2
)
,
{\displaystyle \left(\frac{3+\sqrt5}{4},\,\frac{1+\sqrt5}{2},\,-\frac{1+\sqrt5}{4},\,-\frac{2+\sqrt5}{2}\right),}
(
3
+
5
4
,
1
+
5
2
,
1
+
5
4
,
2
+
5
2
)
,
{\displaystyle \left(\frac{3+\sqrt5}{4},\,\frac{1+\sqrt5}{2},\,\frac{1+\sqrt5}{4},\,\frac{2+\sqrt5}{2}\right),}
(
±
3
+
5
4
,
−
2
+
5
2
,
−
1
+
5
2
,
±
1
+
5
4
)
,
{\displaystyle \left(±\frac{3+\sqrt5}{4},\,-\frac{2+\sqrt5}{2},\,-\frac{1+\sqrt5}{2},\,±\frac{1+\sqrt5}{4}\right),}
(
±
3
+
5
4
,
2
+
5
2
,
1
+
5
2
,
1
+
5
4
)
,
{\displaystyle \left(±\frac{3+\sqrt5}{4},\,\frac{2+\sqrt5}{2},\,\frac{1+\sqrt5}{2},\,\frac{1+\sqrt5}{4}\right),}
(
−
3
+
5
4
,
±
2
+
5
2
,
1
+
5
2
,
−
1
+
5
4
)
,
{\displaystyle \left(-\frac{3+\sqrt5}{4},\,±\frac{2+\sqrt5}{2},\,\frac{1+\sqrt5}{2},\,-\frac{1+\sqrt5}{4}\right),}
(
−
3
+
5
4
,
2
+
5
2
,
−
1
+
5
2
,
−
1
+
5
4
)
,
{\displaystyle \left(-\frac{3+\sqrt5}{4},\,\frac{2+\sqrt5}{2},\,-\frac{1+\sqrt5}{2},\,-\frac{1+\sqrt5}{4}\right),}
(
3
+
5
4
,
−
2
+
5
2
,
1
+
5
2
,
1
+
5
4
)
,
{\displaystyle \left(\frac{3+\sqrt5}{4},\,-\frac{2+\sqrt5}{2},\,\frac{1+\sqrt5}{2},\,\frac{1+\sqrt5}{4}\right),}
(
3
+
5
4
,
2
+
5
2
,
−
1
+
5
2
,
1
+
5
4
)
,
{\displaystyle \left(\frac{3+\sqrt5}{4},\,\frac{2+\sqrt5}{2},\,-\frac{1+\sqrt5}{2},\,\frac{1+\sqrt5}{4}\right),}
(
3
+
5
4
,
2
+
5
2
,
1
+
5
2
,
−
1
+
5
4
)
,
{\displaystyle \left(\frac{3+\sqrt5}{4},\,\frac{2+\sqrt5}{2},\,\frac{1+\sqrt5}{2},\,-\frac{1+\sqrt5}{4}\right),}
(
±
1
+
5
2
,
−
1
+
5
4
,
−
3
+
5
4
,
±
2
+
5
2
)
,
{\displaystyle \left(±\frac{1+\sqrt5}{2},\,-\frac{1+\sqrt5}{4},\,-\frac{3+\sqrt5}{4},\,±\frac{2+\sqrt5}{2}\right),}
(
±
1
+
5
2
,
1
+
5
4
,
3
+
5
4
,
2
+
5
2
)
,
{\displaystyle \left(±\frac{1+\sqrt5}{2},\,\frac{1+\sqrt5}{4},\,\frac{3+\sqrt5}{4},\,\frac{2+\sqrt5}{2}\right),}
(
−
1
+
5
2
,
±
1
+
5
4
,
3
+
5
4
,
−
2
+
5
2
)
,
{\displaystyle \left(-\frac{1+\sqrt5}{2},\,±\frac{1+\sqrt5}{4},\,\frac{3+\sqrt5}{4},\,-\frac{2+\sqrt5}{2}\right),}
(
−
1
+
5
2
,
1
+
5
4
,
−
3
+
5
4
,
−
2
+
5
2
)
,
{\displaystyle \left(-\frac{1+\sqrt5}{2},\,\frac{1+\sqrt5}{4},\,-\frac{3+\sqrt5}{4},\,-\frac{2+\sqrt5}{2}\right),}
(
1
+
5
2
,
−
1
+
5
4
,
3
+
5
4
,
2
+
5
2
)
,
{\displaystyle \left(\frac{1+\sqrt5}{2},\,-\frac{1+\sqrt5}{4},\,\frac{3+\sqrt5}{4},\,\frac{2+\sqrt5}{2}\right),}
(
1
+
5
2
,
1
+
5
4
,
−
3
+
5
4
,
2
+
5
2
)
,
{\displaystyle \left(\frac{1+\sqrt5}{2},\,\frac{1+\sqrt5}{4},\,-\frac{3+\sqrt5}{4},\,\frac{2+\sqrt5}{2}\right),}
(
1
+
5
2
,
1
+
5
4
,
3
+
5
4
,
−
2
+
5
2
)
,
{\displaystyle \left(\frac{1+\sqrt5}{2},\,\frac{1+\sqrt5}{4},\,\frac{3+\sqrt5}{4},\,-\frac{2+\sqrt5}{2}\right),}
(
±
1
+
5
2
,
−
3
+
5
4
,
−
2
+
5
2
,
±
1
+
5
4
)
,
{\displaystyle \left(±\frac{1+\sqrt5}{2},\,-\frac{3+\sqrt5}{4},\,-\frac{2+\sqrt5}{2},\,±\frac{1+\sqrt5}{4}\right),}
(
±
1
+
5
2
,
3
+
5
4
,
2
+
5
2
,
−
1
+
5
4
)
,
{\displaystyle \left(±\frac{1+\sqrt5}{2},\,\frac{3+\sqrt5}{4},\,\frac{2+\sqrt5}{2},\,-\frac{1+\sqrt5}{4}\right),}
(
−
1
+
5
2
,
±
3
+
5
4
,
2
+
5
2
,
1
+
5
4
)
,
{\displaystyle \left(-\frac{1+\sqrt5}{2},\,±\frac{3+\sqrt5}{4},\,\frac{2+\sqrt5}{2},\,\frac{1+\sqrt5}{4}\right),}
(
−
1
+
5
2
,
3
+
5
4
,
−
2
+
5
2
,
1
+
5
4
)
,
{\displaystyle \left(-\frac{1+\sqrt5}{2},\,\frac{3+\sqrt5}{4},\,-\frac{2+\sqrt5}{2},\,\frac{1+\sqrt5}{4}\right),}
(
1
+
5
2
,
−
3
+
5
4
,
2
+
5
2
,
−
1
+
5
4
)
,
{\displaystyle \left(\frac{1+\sqrt5}{2},\,-\frac{3+\sqrt5}{4},\,\frac{2+\sqrt5}{2},\,-\frac{1+\sqrt5}{4}\right),}
(
1
+
5
2
,
3
+
5
4
,
−
2
+
5
2
,
−
1
+
5
4
)
,
{\displaystyle \left(\frac{1+\sqrt5}{2},\,\frac{3+\sqrt5}{4},\,-\frac{2+\sqrt5}{2},\,-\frac{1+\sqrt5}{4}\right),}
(
1
+
5
2
,
3
+
5
4
,
2
+
5
2
,
1
+
5
4
)
,
{\displaystyle \left(\frac{1+\sqrt5}{2},\,\frac{3+\sqrt5}{4},\,\frac{2+\sqrt5}{2},\,\frac{1+\sqrt5}{4}\right),}
(
±
1
+
5
2
,
±
2
+
5
2
,
±
1
+
5
4
,
±
3
+
5
4
)
,
{\displaystyle \left(±\frac{1+\sqrt5}{2},\,±\frac{2+\sqrt5}{2},\,±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{4}\right),}
(
±
2
+
5
2
,
−
1
+
5
4
,
1
+
5
2
,
3
+
5
4
)
,
{\displaystyle \left(±\frac{2+\sqrt5}{2},\,-\frac{1+\sqrt5}{4},\,\frac{1+\sqrt5}{2},\,\frac{3+\sqrt5}{4}\right),}
(
−
2
+
5
2
,
−
1
+
5
4
,
±
1
+
5
2
,
−
3
+
5
4
)
,
{\displaystyle \left(-\frac{2+\sqrt5}{2},\,-\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,-\frac{3+\sqrt5}{4}\right),}
(
−
2
+
5
2
,
1
+
5
4
,
−
1
+
5
2
,
±
3
+
5
4
)
,
{\displaystyle \left(-\frac{2+\sqrt5}{2},\,\frac{1+\sqrt5}{4},\,-\frac{1+\sqrt5}{2},\,±\frac{3+\sqrt5}{4}\right),}
(
−
2
+
5
2
,
1
+
5
4
,
1
+
5
2
,
−
3
+
5
4
)
,
{\displaystyle \left(-\frac{2+\sqrt5}{2},\,\frac{1+\sqrt5}{4},\,\frac{1+\sqrt5}{2},\,-\frac{3+\sqrt5}{4}\right),}
(
2
+
5
2
,
±
1
+
5
4
,
−
1
+
5
2
,
3
+
5
4
)
,
{\displaystyle \left(\frac{2+\sqrt5}{2},\,±\frac{1+\sqrt5}{4},\,-\frac{1+\sqrt5}{2},\,\frac{3+\sqrt5}{4}\right),}
(
2
+
5
2
,
−
1
+
5
4
,
1
+
5
2
,
−
3
+
5
4
)
,
{\displaystyle \left(\frac{2+\sqrt5}{2},\,-\frac{1+\sqrt5}{4},\,\frac{1+\sqrt5}{2},\,-\frac{3+\sqrt5}{4}\right),}
(
2
+
5
2
,
1
+
5
4
,
−
1
+
5
2
,
−
3
+
5
4
)
,
{\displaystyle \left(\frac{2+\sqrt5}{2},\,\frac{1+\sqrt5}{4},\,-\frac{1+\sqrt5}{2},\,-\frac{3+\sqrt5}{4}\right),}
(
2
+
5
2
,
1
+
5
4
,
1
+
5
2
,
3
+
5
4
)
,
{\displaystyle \left(\frac{2+\sqrt5}{2},\,\frac{1+\sqrt5}{4},\,\frac{1+\sqrt5}{2},\,\frac{3+\sqrt5}{4}\right),}
(
±
2
+
5
2
,
−
3
+
5
4
,
1
+
5
4
,
−
1
+
5
2
)
,
{\displaystyle \left(±\frac{2+\sqrt5}{2},\,-\frac{3+\sqrt5}{4},\,\frac{1+\sqrt5}{4},\,-\frac{1+\sqrt5}{2}\right),}
(
−
2
+
5
2
,
−
3
+
5
4
,
±
1
+
5
4
,
1
+
5
2
)
,
{\displaystyle \left(-\frac{2+\sqrt5}{2},\,-\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,\frac{1+\sqrt5}{2}\right),}
(
−
2
+
5
2
,
3
+
5
4
,
−
1
+
5
4
,
±
1
+
5
2
)
,
{\displaystyle \left(-\frac{2+\sqrt5}{2},\,\frac{3+\sqrt5}{4},\,-\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{2}\right),}
(
−
2
+
5
2
,
3
+
5
4
,
1
+
5
4
,
1
+
5
2
)
,
{\displaystyle \left(-\frac{2+\sqrt5}{2},\,\frac{3+\sqrt5}{4},\,\frac{1+\sqrt5}{4},\,\frac{1+\sqrt5}{2}\right),}
(
2
+
5
2
,
±
3
+
5
4
,
−
1
+
5
4
,
−
1
+
5
2
)
,
{\displaystyle \left(\frac{2+\sqrt5}{2},\,±\frac{3+\sqrt5}{4},\,-\frac{1+\sqrt5}{4},\,-\frac{1+\sqrt5}{2}\right),}
(
2
+
5
2
,
−
3
+
5
4
,
1
+
5
4
,
1
+
5
2
)
,
{\displaystyle \left(\frac{2+\sqrt5}{2},\,-\frac{3+\sqrt5}{4},\,\frac{1+\sqrt5}{4},\,\frac{1+\sqrt5}{2}\right),}
(
2
+
5
2
,
3
+
5
4
,
−
1
+
5
4
,
1
+
5
2
)
,
{\displaystyle \left(\frac{2+\sqrt5}{2},\,\frac{3+\sqrt5}{4},\,-\frac{1+\sqrt5}{4},\,\frac{1+\sqrt5}{2}\right),}
(
2
+
5
2
,
3
+
5
4
,
1
+
5
4
,
−
1
+
5
2
)
,
{\displaystyle \left(\frac{2+\sqrt5}{2},\,\frac{3+\sqrt5}{4},\,\frac{1+\sqrt5}{4},\,-\frac{1+\sqrt5}{2}\right),}
(
±
2
+
5
2
,
±
1
+
5
2
,
±
3
+
5
4
,
±
1
+
5
4
)
.
{\displaystyle \left(±\frac{2+\sqrt5}{2},\,±\frac{1+\sqrt5}{2},\,±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{4}\right).}
These are derived by removing 120 vertices from the rectified hexacosichoron .
