Octagonal duoexpandoprism

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Octagonal duoexpandoprism
Rank4
TypeIsogonal
Notation
Bowers style acronymOdep
Coxeter diagramxo8xx ox8xx&#zy
Elements
Cells64 tetragonal disphenoids, 128 wedges, 64 rectangular trapezoprisms, 16+16 octagonal prisms
Faces256 isosceles triangles, 256 isosceles trapezoids, 128+128 rectangles, 32 octagons
Edges128+128+256+256
Vertices256
Vertex figureMirror-symmetric triangular antiprism
Measures (based on two octagonal-hexadecagonal duoprisms of edge length 1)
Edge lengthsEdges of duoprisms (128+128+256): 1
 Lacing edges (256):
Circumradius
Central density1
Related polytopes
ArmyOdep
RegimentOdep
DualOctagonal duoexpandotegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(8)≀S2, order 512
ConvexYes
NatureTame

The octagonal duoexpandoprism or odep is a convex isogonal polychoron and the seventh member of the duoexpandoprism family. It consists of 32 octagonal prisms of two kinds, 64 rectangular trapezoprisms, 128 wedges and 64 tetragonal disphenoids. 2 octagonal prisms, 1 tetragonal disphenoid, 3 wedges, and 2 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two orthogonal octagonal-hexadecagonal duoprisms, or more generally octagonal-dioctagonal duoprisms, and a subset of its variations can be formed by expanding the cell of the octagonal duoprism outward. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is .