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
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±
2
2
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2
2
2
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,
{\displaystyle \left(0,\,0,\,±\frac{\sqrt2}{2},\,±\frac{\sqrt{10}-2\sqrt2}{2}\right),}
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±
2
4
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±
2
4
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2
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2
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3
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4
)
,
{\displaystyle \left(±\frac{\sqrt2}{4},\,±\frac{\sqrt2}{4},\,±\frac{\sqrt{10}-2\sqrt2}{4},\,±\frac{2\sqrt{10}-3\sqrt2}{4}\right),}
(
±
10
−
2
8
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±
10
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2
8
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3
10
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2
8
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7
2
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3
10
8
)
,
{\displaystyle \left(±\frac{\sqrt{10}-\sqrt2}{8},\,±\frac{\sqrt{10}-\sqrt2}{8},\,±3\frac{\sqrt{10}-\sqrt2}{8},\,±\frac{7\sqrt2-3\sqrt{10}}{8}\right),}
(
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3
2
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10
8
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3
2
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10
8
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2
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10
8
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3
3
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10
8
)
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{\displaystyle \left(±\frac{3\sqrt2-\sqrt{10}}{8},\,±\frac{3\sqrt2-\sqrt{10}}{8},\,±\frac{\sqrt2+\sqrt{10}}{8},\,±3\frac{3\sqrt2-\sqrt{10}}{8}\right),}
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±
10
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2
4
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±
10
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2
4
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3
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10
4
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±
3
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10
4
)
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{\displaystyle \left(±\frac{\sqrt{10}-\sqrt2}{4},\,±\frac{\sqrt{10}-\sqrt2}{4},\,±\frac{3\sqrt2-\sqrt{10}}{4},\,±\frac{3\sqrt2-\sqrt{10}}{4}\right),}
(
±
5
2
−
10
8
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±
5
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10
8
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±
10
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2
8
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7
2
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3
10
8
)
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{\displaystyle \left(±\frac{5\sqrt2-\sqrt{10}}{8},\,±\frac{5\sqrt2-\sqrt{10}}{8},\,±\frac{\sqrt{10}-\sqrt2}{8},\,±\frac{7\sqrt2-3\sqrt{10}}{8}\right),}
(
±
10
−
2
2
4
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±
10
−
2
2
4
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±
2
4
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±
4
2
−
10
4
)
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{\displaystyle \left(±\frac{\sqrt{10}-2\sqrt2}{4},\,±\frac{\sqrt{10}-2\sqrt2}{4},\,±\frac{\sqrt2}{4},\,±\frac{4\sqrt2-\sqrt{10}}{4}\right),}
(
±
3
10
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5
2
8
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±
3
10
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5
2
8
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±
2
+
10
8
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±
3
2
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10
8
)
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{\displaystyle \left(±\frac{3\sqrt{10}-5\sqrt2}{8},\,±\frac{3\sqrt{10}-5\sqrt2}{8},\,±\frac{\sqrt2+\sqrt{10}}{8},\,±\frac{3\sqrt2-\sqrt{10}}{8}\right),}
together with all even permutations of:
(
0
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±
2
4
,
±
5
2
−
10
8
,
±
3
3
2
−
10
8
)
,
{\displaystyle \left(0,\,±\frac{\sqrt2}{4},\,±\frac{5\sqrt2-\sqrt{10}}{8},\,±3\frac{3\sqrt2-\sqrt{10}}{8}\right),}
(
0
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±
3
2
−
10
8
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±
2
10
−
3
2
4
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±
5
2
−
10
8
)
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{\displaystyle \left(0,\,±\frac{3\sqrt2-\sqrt{10}}{8},\,±\frac{2\sqrt{10}-3\sqrt2}{4},\,±\frac{5\sqrt2-\sqrt{10}}{8}\right),}
(
0
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±
10
−
2
8
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±
3
10
−
5
2
8
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±
4
2
−
10
4
)
,
{\displaystyle \left(0,\,±\frac{\sqrt{10}-\sqrt2}{8},\,±\frac{3\sqrt{10}-5\sqrt2}{8},\,±\frac{4\sqrt2-\sqrt{10}}{4}\right),}
(
0
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±
10
−
2
2
4
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±
3
10
−
2
8
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±
3
10
−
5
2
8
)
,
{\displaystyle \left(0,\,±\frac{\sqrt{10}-2\sqrt2}{4},\,±3\frac{\sqrt{10}-\sqrt2}{8},\,±\frac{3\sqrt{10}-5\sqrt2}{8}\right),}
(
±
2
+
10
8
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±
2
4
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±
10
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2
2
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±
10
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2
8
)
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{\displaystyle \left(±\frac{\sqrt2+\sqrt{10}}{8},\,±\frac{\sqrt2}{4},\,±\frac{\sqrt{10}-\sqrt2}{2},\,±\frac{\sqrt{10}-\sqrt2}{8}\right),}
(
±
2
+
10
8
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±
2
4
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3
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10
4
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7
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{\displaystyle \left(±\frac{\sqrt2+\sqrt{10}}{8},\,±\frac{\sqrt2}{4},\,±\frac{3\sqrt2-\sqrt{10}}{4},\,±\frac{7\sqrt2-3\sqrt{10}}{8}\right),}
(
±
2
+
10
8
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±
10
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2
4
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±
7
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3
10
8
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2
10
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2
4
)
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{\displaystyle \left(±\frac{\sqrt2+\sqrt{10}}{8},\,±\frac{\sqrt{10}-\sqrt2}{4},\,±\frac{7\sqrt2-3\sqrt{10}}{8},\,±\frac{2\sqrt{10}-\sqrt2}{4}\right),}
(
±
2
4
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±
10
−
2
8
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±
10
−
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4
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±
3
3
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−
10
8
)
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{\displaystyle \left(±\frac{\sqrt2}{4},\,±\frac{\sqrt{10}-\sqrt2}{8},\,±\frac{\sqrt{10}-\sqrt2}{4},\,±3\frac{3\sqrt2-\sqrt{10}}{8}\right),}
(
±
2
4
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±
5
2
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10
8
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±
3
2
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10
4
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±
3
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5
2
8
)
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{\displaystyle \left(±\frac{\sqrt2}{4},\,±\frac{5\sqrt2-\sqrt{10}}{8},\,±\frac{3\sqrt2-\sqrt{10}}{4},\,±\frac{3\sqrt{10}-5\sqrt2}{8}\right),}
(
±
10
−
2
8
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±
3
2
−
10
8
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±
10
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2
4
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±
2
10
−
3
2
4
)
,
{\displaystyle \left(±\frac{\sqrt{10}-\sqrt2}{8},\,±\frac{3\sqrt2-\sqrt{10}}{8},\,±\frac{\sqrt{10}-\sqrt2}{4},\,±\frac{2\sqrt{10}-3\sqrt2}{4}\right),}
(
±
10
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2
8
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±
3
2
−
10
8
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±
3
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−
10
4
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±
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10
4
)
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{\displaystyle \left(±\frac{\sqrt{10}-\sqrt2}{8},\,±\frac{3\sqrt2-\sqrt{10}}{8},\,±\frac{3\sqrt2-\sqrt{10}}{4},\,±\frac{4\sqrt2-\sqrt{10}}{4}\right),}
(
±
2
2
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±
3
2
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10
8
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±
10
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2
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±
7
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3
10
8
)
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{\displaystyle \left(±\frac{\sqrt2}{2},\,±\frac{3\sqrt2-\sqrt{10}}{8},\,±\frac{\sqrt{10}-2\sqrt2}{4},\,±\frac{7\sqrt2-3\sqrt{10}}{8}\right),}
(
±
3
2
−
10
8
,
±
10
−
2
2
4
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±
3
2
−
10
4
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±
3
10
−
2
8
)
,
{\displaystyle \left(±\frac{3\sqrt2-\sqrt{10}}{8},\,±\frac{\sqrt{10}-2\sqrt2}{4},\,±\frac{3\sqrt2-\sqrt{10}}{4},\,±3\frac{\sqrt{10}-\sqrt2}{8}\right),}
(
±
10
−
2
4
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±
5
2
−
10
8
,
±
3
10
−
5
2
8
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±
10
−
2
2
4
)
.
{\displaystyle \left(±\frac{\sqrt{10}-\sqrt2}{4},\,±\frac{5\sqrt2-\sqrt{10}}{8},\,±\frac{3\sqrt{10}-5\sqrt2}{8},\,±\frac{\sqrt{10}-2\sqrt2}{4}\right).}
