The great disnub dishexacosichoron , or gadsadox , is a nonconvex uniform polychoron that consists of 4800 regular octahedra (falling in pairs into the same hyperplane, thus forming 2400 golden hexagrammic antiprisms ) and 1200 regular great icosahedra (also falling in pairs in the same hyperplane, forming 600 small retrosnub disoctahedra ). 8 octahedra and 4 great icosahedra join at each vertex.
This polychoron can be obtained as the blend of 10 rectified grand hexacosichora . In the process some of the octahedra blend out fully, while the other cells compound as noted above. In addition the vertex figure would in turn be a blend of two pentagrammic prismatic vertex figures of the rectified grand hexacosichoron.
Coordinates for the vertices of a great disnub dishexacosichoron of edge length 1 are given by all permutations of:
(
0
,
0
,
±
2
2
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±
10
−
2
2
2
)
,
{\displaystyle \left(0,\,0,\,\pm {\frac {\sqrt {2}}{2}},\,\pm {\frac {{\sqrt {10}}-2{\sqrt {2}}}{2}}\right),}
(
±
2
4
,
±
2
4
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±
10
−
2
2
4
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±
2
10
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3
2
4
)
,
{\displaystyle \left(\pm {\frac {\sqrt {2}}{4}},\,\pm {\frac {\sqrt {2}}{4}},\,\pm {\frac {{\sqrt {10}}-2{\sqrt {2}}}{4}},\,\pm {\frac {2{\sqrt {10}}-3{\sqrt {2}}}{4}}\right),}
(
±
10
−
2
8
,
±
10
−
2
8
,
±
3
10
−
2
8
,
±
7
2
−
3
10
8
)
,
{\displaystyle \left(\pm {\frac {{\sqrt {10}}-{\sqrt {2}}}{8}},\,\pm {\frac {{\sqrt {10}}-{\sqrt {2}}}{8}},\,\pm 3{\frac {{\sqrt {10}}-{\sqrt {2}}}{8}},\,\pm {\frac {7{\sqrt {2}}-3{\sqrt {10}}}{8}}\right),}
(
±
3
2
−
10
8
,
±
3
2
−
10
8
,
±
2
+
10
8
,
±
3
3
2
−
10
8
)
,
{\displaystyle \left(\pm {\frac {3{\sqrt {2}}-{\sqrt {10}}}{8}},\,\pm {\frac {3{\sqrt {2}}-{\sqrt {10}}}{8}},\,\pm {\frac {{\sqrt {2}}+{\sqrt {10}}}{8}},\,\pm 3{\frac {3{\sqrt {2}}-{\sqrt {10}}}{8}}\right),}
(
±
10
−
2
4
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±
10
−
2
4
,
±
3
2
−
10
4
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±
3
2
−
10
4
)
,
{\displaystyle \left(\pm {\frac {{\sqrt {10}}-{\sqrt {2}}}{4}},\,\pm {\frac {{\sqrt {10}}-{\sqrt {2}}}{4}},\,\pm {\frac {3{\sqrt {2}}-{\sqrt {10}}}{4}},\,\pm {\frac {3{\sqrt {2}}-{\sqrt {10}}}{4}}\right),}
(
±
5
2
−
10
8
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±
5
2
−
10
8
,
±
10
−
2
8
,
±
7
2
−
3
10
8
)
,
{\displaystyle \left(\pm {\frac {5{\sqrt {2}}-{\sqrt {10}}}{8}},\,\pm {\frac {5{\sqrt {2}}-{\sqrt {10}}}{8}},\,\pm {\frac {{\sqrt {10}}-{\sqrt {2}}}{8}},\,\pm {\frac {7{\sqrt {2}}-3{\sqrt {10}}}{8}}\right),}
(
±
10
−
2
2
4
,
±
10
−
2
2
4
,
±
2
4
,
±
4
2
−
10
4
)
,
{\displaystyle \left(\pm {\frac {{\sqrt {10}}-2{\sqrt {2}}}{4}},\,\pm {\frac {{\sqrt {10}}-2{\sqrt {2}}}{4}},\,\pm {\frac {\sqrt {2}}{4}},\,\pm {\frac {4{\sqrt {2}}-{\sqrt {10}}}{4}}\right),}
(
±
3
10
−
5
2
8
,
±
3
10
−
5
2
8
,
±
2
+
10
8
,
±
3
2
−
10
8
)
,
{\displaystyle \left(\pm {\frac {3{\sqrt {10}}-5{\sqrt {2}}}{8}},\,\pm {\frac {3{\sqrt {10}}-5{\sqrt {2}}}{8}},\,\pm {\frac {{\sqrt {2}}+{\sqrt {10}}}{8}},\,\pm {\frac {3{\sqrt {2}}-{\sqrt {10}}}{8}}\right),}
together with all even permutations of:
(
0
,
±
2
4
,
±
5
2
−
10
8
,
±
3
3
2
−
10
8
)
,
{\displaystyle \left(0,\,\pm {\frac {\sqrt {2}}{4}},\,\pm {\frac {5{\sqrt {2}}-{\sqrt {10}}}{8}},\,\pm 3{\frac {3{\sqrt {2}}-{\sqrt {10}}}{8}}\right),}
(
0
,
±
3
2
−
10
8
,
±
2
10
−
3
2
4
,
±
5
2
−
10
8
)
,
{\displaystyle \left(0,\,\pm {\frac {3{\sqrt {2}}-{\sqrt {10}}}{8}},\,\pm {\frac {2{\sqrt {10}}-3{\sqrt {2}}}{4}},\,\pm {\frac {5{\sqrt {2}}-{\sqrt {10}}}{8}}\right),}
(
0
,
±
10
−
2
8
,
±
3
10
−
5
2
8
,
±
4
2
−
10
4
)
,
{\displaystyle \left(0,\,\pm {\frac {{\sqrt {10}}-{\sqrt {2}}}{8}},\,\pm {\frac {3{\sqrt {10}}-5{\sqrt {2}}}{8}},\,\pm {\frac {4{\sqrt {2}}-{\sqrt {10}}}{4}}\right),}
(
0
,
±
10
−
2
2
4
,
±
3
10
−
2
8
,
±
3
10
−
5
2
8
)
,
{\displaystyle \left(0,\,\pm {\frac {{\sqrt {10}}-2{\sqrt {2}}}{4}},\,\pm 3{\frac {{\sqrt {10}}-{\sqrt {2}}}{8}},\,\pm {\frac {3{\sqrt {10}}-5{\sqrt {2}}}{8}}\right),}
(
±
2
+
10
8
,
±
2
4
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±
10
−
2
2
,
±
10
−
2
8
)
,
{\displaystyle \left(\pm {\frac {{\sqrt {2}}+{\sqrt {10}}}{8}},\,\pm {\frac {\sqrt {2}}{4}},\,\pm {\frac {{\sqrt {10}}-{\sqrt {2}}}{2}},\,\pm {\frac {{\sqrt {10}}-{\sqrt {2}}}{8}}\right),}
(
±
2
+
10
8
,
±
2
4
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±
3
2
−
10
4
,
±
7
2
−
3
10
8
)
,
{\displaystyle \left(\pm {\frac {{\sqrt {2}}+{\sqrt {10}}}{8}},\,\pm {\frac {\sqrt {2}}{4}},\,\pm {\frac {3{\sqrt {2}}-{\sqrt {10}}}{4}},\,\pm {\frac {7{\sqrt {2}}-3{\sqrt {10}}}{8}}\right),}
(
±
2
+
10
8
,
±
10
−
2
4
,
±
7
2
−
3
10
8
,
±
2
10
−
2
4
)
,
{\displaystyle \left(\pm {\frac {{\sqrt {2}}+{\sqrt {10}}}{8}},\,\pm {\frac {{\sqrt {10}}-{\sqrt {2}}}{4}},\,\pm {\frac {7{\sqrt {2}}-3{\sqrt {10}}}{8}},\,\pm {\frac {2{\sqrt {10}}-{\sqrt {2}}}{4}}\right),}
(
±
2
4
,
±
10
−
2
8
,
±
10
−
2
4
,
±
3
3
2
−
10
8
)
,
{\displaystyle \left(\pm {\frac {\sqrt {2}}{4}},\,\pm {\frac {{\sqrt {10}}-{\sqrt {2}}}{8}},\,\pm {\frac {{\sqrt {10}}-{\sqrt {2}}}{4}},\,\pm 3{\frac {3{\sqrt {2}}-{\sqrt {10}}}{8}}\right),}
(
±
2
4
,
±
5
2
−
10
8
,
±
3
2
−
10
4
,
±
3
10
−
5
2
8
)
,
{\displaystyle \left(\pm {\frac {\sqrt {2}}{4}},\,\pm {\frac {5{\sqrt {2}}-{\sqrt {10}}}{8}},\,\pm {\frac {3{\sqrt {2}}-{\sqrt {10}}}{4}},\,\pm {\frac {3{\sqrt {10}}-5{\sqrt {2}}}{8}}\right),}
(
±
10
−
2
8
,
±
3
2
−
10
8
,
±
10
−
2
4
,
±
2
10
−
3
2
4
)
,
{\displaystyle \left(\pm {\frac {{\sqrt {10}}-{\sqrt {2}}}{8}},\,\pm {\frac {3{\sqrt {2}}-{\sqrt {10}}}{8}},\,\pm {\frac {{\sqrt {10}}-{\sqrt {2}}}{4}},\,\pm {\frac {2{\sqrt {10}}-3{\sqrt {2}}}{4}}\right),}
(
±
10
−
2
8
,
±
3
2
−
10
8
,
±
3
2
−
10
4
,
±
4
2
−
10
4
)
,
{\displaystyle \left(\pm {\frac {{\sqrt {10}}-{\sqrt {2}}}{8}},\,\pm {\frac {3{\sqrt {2}}-{\sqrt {10}}}{8}},\,\pm {\frac {3{\sqrt {2}}-{\sqrt {10}}}{4}},\,\pm {\frac {4{\sqrt {2}}-{\sqrt {10}}}{4}}\right),}
(
±
2
2
,
±
3
2
−
10
8
,
±
10
−
2
2
4
,
±
7
2
−
3
10
8
)
,
{\displaystyle \left(\pm {\frac {\sqrt {2}}{2}},\,\pm {\frac {3{\sqrt {2}}-{\sqrt {10}}}{8}},\,\pm {\frac {{\sqrt {10}}-2{\sqrt {2}}}{4}},\,\pm {\frac {7{\sqrt {2}}-3{\sqrt {10}}}{8}}\right),}
(
±
3
2
−
10
8
,
±
10
−
2
2
4
,
±
3
2
−
10
4
,
±
3
10
−
2
8
)
,
{\displaystyle \left(\pm {\frac {3{\sqrt {2}}-{\sqrt {10}}}{8}},\,\pm {\frac {{\sqrt {10}}-2{\sqrt {2}}}{4}},\,\pm {\frac {3{\sqrt {2}}-{\sqrt {10}}}{4}},\,\pm 3{\frac {{\sqrt {10}}-{\sqrt {2}}}{8}}\right),}
(
±
10
−
2
4
,
±
5
2
−
10
8
,
±
3
10
−
5
2
8
,
±
10
−
2
2
4
)
.
{\displaystyle \left(\pm {\frac {{\sqrt {10}}-{\sqrt {2}}}{4}},\,\pm {\frac {5{\sqrt {2}}-{\sqrt {10}}}{8}},\,\pm {\frac {3{\sqrt {10}}-5{\sqrt {2}}}{8}},\,\pm {\frac {{\sqrt {10}}-2{\sqrt {2}}}{4}}\right).}