Digonal duotruncatoalterantiprism

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Digonal duotruncatoalterantiprism
File:Digonal duotruncatoalterantiprism.png
Rank4
TypeIsogonal
Elements
Cells16 digonal disphenoids, 8+16 tetragonal disphenoids, 32 isosceles trapezoidal pyramids, 16 wedges
Faces32+32+32+64 isosceles triangles, 32 isosceles trapezoids, 8 rectangles
Edges16+16+16+32+64
Vertices32
Vertex figurePolyhedron with 1 tetragon and 12 triangles
Measures (edge length 1)
Central density1
Related polytopes
DualDigonal duotruncatoalterantitegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryB2+≀S2×2, order 64
ConvexYes
NatureTame

The digonal duotruncatoalterantiprism is a convex isogonal polychoron and the first member of the duotruncatoalterantiprisms. It consists of 16 wedges, 32 isosceles trapezoidal pyramids, 24 tetragonal disphenoids of two kinds, and 16 digonal disphenoids. 3 wedges, 5 isosceles trapezoidal pyramids, 3 tetragonal disphenoids, and 2 digonal disphenoids join at each vertex. It can be obtained as the convex hull of two orthogonal digonal-square prismantiprismoids. However, it cannot be made scaliform.

This polychoron cannot be optimized using the ratio method, because the solution (with intended minimal ratio 1: ≈ 1:1.41421) would yield a rectified tesseract instead.