# Octagonal antiditetragoltriate

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Octagonal antiditetragoltriate
Rank4
TypeIsogonal
Notation
Bowers style acronymOadet
Elements
Cells64+64 tetragonal disphenoids, 128 rectangular pyramids, 16 octagonal prisms
Faces256+256 isosceles triangles, 128 rectangles, 16 octagons
Edges128+128+256
Vertices128
Vertex figureBiaugmented triangular prism
Measures (based on same duoprisms as optimized octagonal ditetragoltriate)
Edge lengthsEdges of smaller octagon (128): 1
Lacing edges (256): ${\displaystyle {\sqrt {3+{\sqrt {2}}-{\sqrt {4+2{\sqrt {2}}}}}}\approx 1.34205}$
Edges of larger octagon (128): ${\displaystyle {\frac {2+{\sqrt {4-2{\sqrt {2}}}}}{2}}\approx 1.54120}$
Circumradius${\displaystyle {\sqrt {\frac {5+2{\sqrt {2}}+2{\sqrt {2+{\sqrt {2}}}}}{2}}}\approx 2.40041}$
Central density1
Related polytopes
ArmyOadet
RegimentOadet
DualOctagonal antitetrambitriate
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(8)≀S2, order 512
ConvexYes
NatureTame

The octagonal antiditetragoltriate or oadet is a convex isogonal polychoron and the sixth member of the antiditetragoltriate family. It consists of 16 octagonal prisms, 128 rectangular pyramids, and 128 tetragonal disphenoids of two kinds. 2 octagonal prisms, 4 tetragonal disphenoids, and 5 rectangular pyramids join at each vertex. However, it cannot be made scaliform.

It can be formed as the convex hull of 2 oppositely oriented semi-uniform octagonal duoprisms where the larger octagon is more than ${\displaystyle {\sqrt {4-2{\sqrt {2}}}}}$ times the edge length of the smaller one.