Enneagonal-truncated cubic duoprism

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Enneagonal-truncated cubic duoprism
Rank5
TypeUniform
Notation
Bowers style acronymEtic
Coxeter diagramx9o x4x3o ()
Elements
Tera8 triangular-enneagonal duoprisms, 9 truncated cubic prisms, 6 octagonal-enneagonal duoprisms
Cells72 triangular prisms, 54 octagonal prisms, 12+24 enneagonal prisms, 9 truncated cubes
Faces72 triangles, 108+216 squares, 54 octagons, 24 enneagons
Edges108+216+216
Vertices216
Vertex figureDigonal disphenoidal pyramid, edge lengths 1, 2+2, 2+2 (base triangle), cos(π/9) (top), 2 (side edges)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesTiccup–tic–ticcup: 140°
 Tedip–ep–oedip:
 Tedip–trip–ticcup: 90°
 Oedip–op–ticcup: 90°
 Oedip–ep–oedip: 90°
Central density1
Number of external pieces23
Level of complexity30
Related polytopes
ArmyEtic
RegimentEtic
DualEnneagonal-triakis octahedral duotegum
ConjugatesEnneagrammic-truncated cubic duoprism, Great enneagrammic-truncated cubic duoprism, Enneagonal-quasitruncated hexahedral duoprism, Enneagrammic-quasitruncated hexahedral duoprism, Great enneagrammic-quasitruncated hexahedral duoprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryB3×I2(9), order 864
ConvexYes
NatureTame

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.

Vertex coordinates[edit | edit source]

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.