Triangular-hexagonal prismantiprismoid

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Triangular-hexagonal prismantiprismoid
Rank4
TypeIsogonal
SpaceSpherical
Bowers style acronymThipap
Coxeter diagramx6s2s6o (CDel node 1.pngCDel 6.pngCDel node h.pngCDel 2.pngCDel node h.pngCDel 6.pngCDel node.png)
Elements
Vertex figureMonoaugmented rectangular pyramid
Cells18 wedges, 6 triangular prisms, 6 triangular antiprisms, 6 ditrigonal trapezoprisms
Faces36 isosceles triangles, 12 triangles, 36 isosceles trapezoids, 18 rectangles, 6 ditrigons
Edges18+18+36+36
Vertices36
Measures (as derived from unit-edge hexagonal-dodecagonal duoprism)
Edge lengthsShort edges of ditrigons (18): 1
 Side edges (36):
 Edges of triangles (36):
 Long edges of ditrigons (12):
Circumradius
Central density1
Euler characteristic0
Related polytopes
ArmyThipap
RegimentThipap
DualTriangular-hexagonal tegmantitegmoid
Topological properties
OrientableYes
Properties
Symmetry(G2×G2)/2, order 72
ConvexYes
NatureTame

The triangular-hexagonal prismantiprismoid or thipap, also known as the edge-snub triangular-hexagonal duoprism or 3-6 prismantiprismoid, is a convex isogonal polychoron that consists of 6 ditrigonal trapezoprisms, 6 triangular antiprisms, 6 triangular prisms, and 18 wedges. 1 triangular prism, 1 triangular antiprism, 2 ditrigonal trapezoprisms, and 3 wedges join at each vertex. It can be obtained through the process of alternating one class of edges of the hexagonal-dodecagonal duoprism so that the dodecagons become ditrigons. However, it cannot be made uniform, as it generally has 4 edge lengths, which can be minimized to no fewer than 2 different sizes.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.61803.

Vertex coordinates[edit | edit source]

The vertices of a triangular-hexagonal prismantiprismoid, assuming that the triangular antiprisms and triangular prisms are uniform of edge length 1, centered at the origin, are given by:

An alternate set of coordinates, assuming that the edge length differences are minimized, centered at the origin, are given by:

A variant based on a uniform hexagonal-dodecagonal duoprism has vertices given by: