Enneagonal-truncated cubic duoprism |
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Rank | 5 |
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Type | Uniform |
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Notation |
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Bowers style acronym | Etic |
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Coxeter diagram | x9o x4x3o () |
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Elements |
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Tera | 8 triangular-enneagonal duoprisms, 9 truncated cubic prisms, 6 octagonal-enneagonal duoprisms |
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Cells | 72 triangular prisms, 54 octagonal prisms, 12+24 enneagonal prisms, 9 truncated cubes |
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Faces | 72 triangles, 108+216 squares, 54 octagons, 24 enneagons |
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Edges | 108+216+216 |
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Vertices | 216 |
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Vertex figure | Digonal disphenoidal pyramid, edge lengths 1, √2+√2, √2+√2 (base triangle), cos(π/9) (top), √2 (side edges) |
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Measures (edge length 1) |
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Circumradius | |
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Hypervolume | |
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Diteral angles | Ticcup–tic–ticcup: 140° |
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| Tedip–ep–oedip: |
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| Tedip–trip–ticcup: 90° |
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| Oedip–op–ticcup: 90° |
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| Oedip–ep–oedip: 90° |
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Central density | 1 |
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Number of external pieces | 23 |
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Level of complexity | 30 |
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Related polytopes |
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Army | Etic |
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Regiment | Etic |
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Dual | Enneagonal-triakis octahedral duotegum |
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Conjugates | Enneagrammic-truncated cubic duoprism, Great enneagrammic-truncated cubic duoprism, Enneagonal-quasitruncated hexahedral duoprism, Enneagrammic-quasitruncated hexahedral duoprism, Great enneagrammic-quasitruncated hexahedral duoprism |
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Abstract & topological properties |
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Euler characteristic | 2 |
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Orientable | Yes |
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Properties |
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Symmetry | B3×I2(9), order 864 |
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Convex | Yes |
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Nature | Tame |
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The enneagonal-truncated cubic duoprism or etic is a convex uniform duoprism that consists of 9 truncated cubic prisms, 6 octagonal-enneagonal duoprisms, and 8 triangular-enneagonal duoprisms. Each vertex joins 2 truncated cubic prisms, 1 triangular-enneagonal duoprism, and 2 octagonal-enneagonal duoprisms.
The vertices of an enneagonal-truncated cubic duoprism of edge length 2sin(π/9) are given by all permutations of the last three coordinates of:
where j = 2, 4, 8.