Great triangular double gyroprismantiprismoid

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Great triangular double gyroprismantiprismoid
File:Great triangular double gyroprismantiprismoid.png
Rank4
TypeIsogonal
Elements
Cells36 rhombic disphenoids, 18+18 tetragonal disphenoids, 72 isosceles trapezoidal pyramids, 36 wedges, 12 triangular prisms, 12 triangular antiprisms
Faces144 scalene triangles, 72+72+72 isosceles triangles, 24 triangles, 72 isosceles trapezoids, 36 rectangles
Edges36+36+72+72+72+72
Vertices72
Vertex figure10-vertex polyhedron with 2 tetragons and 12 triangles
Measures (edge length 1)
Central density1
Related polytopes
DualGreat triangular double gyrotegmantitegmoid
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
Symmetry(G2≀S2)/2, order 144
ConvexYes
NatureTame

The great triangular double gyroprismantiprismoid is a convex isogonal polychoron and the second member of the double gyroprismantiprismoid family. It consists of 12 triangular antiprisms, 12 triangular prisms, 36 wedges, 72 isosceles trapezoidal pyramids, 36 tetragonal disphenoids of two kinds, and 36 digonal disphenoids. 1 triangular prism, 1 triangular antiporism, 3 wedges, 5 isosceles trapezoidal pyramids, 2 tetragonal disphenoids, and 2 rhombic disphenoids join at each vertex. It can be obtained as the convex hull of two orthogonal triangular-hexagonal prismantiprismoids. However, it cannot be made scaliform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.67303.