Digonal-octagonal tetraprismantiprismoid

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Digonal-octagonal tetraprismantiprismoid
File:Digonal-octagonal tetraprismantiprismoid.png
Rank4
TypeIsogonal
Elements
Cells16+16 phyllic disphenoids, 8 rhombic disphenoids, 16 digonal-rectangular gyrowedges, 8 rectangular gyroprisms
Faces32+32+32+32+32 scalene triangles, 8+8 rectangles
Edges16+16+16+16+16+16+16+32
Vertices32
Vertex figure9-vertex polyhedron with 4 tetragons and 6 triangles
Measures (edge length 1)
Central density1
Related polytopes
DualDigonal-octagonal tetrategmoantitegmoid
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
Symmetry(I2(8)×I2(8))+/4, order 32
ConvexYes
NatureTame

The digonal-octagonal tetraprismantiprismoid is a convex isogonal polychoron that consists of 8 rectangular gyroprisms, 16 digonal-rectangular gyrowedges, 8 rhombic disphenoids, and 32 phyllic disphenoids of two kinds. 1 rhombic disphenoid, 4 phyllic disphenoids, 2 rectangular gyroprisms, and 4 digonal-rectangular gyrowedges join at each vertex. It can be obtained as a subsymmetrical faceting of the octagonal-dioctagonal duoprism. However, it cannot be made scaliform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:2.60607.

Vertex coordinates[edit | edit source]

The vertices of a digonal-octagonal tetraprismantiprismoid, assuming that the edge length differences are minimized, using the ratio method, are given by all even permutations of the first two coordinates of: