Triangular-square prismantiprismoid

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Triangular-square prismantiprismoid
Rank4
TypeIsogonal
SpaceSpherical
Bowers style acronymTispap
Coxeter diagramx4s2s6o (CDel node 1.pngCDel 4.pngCDel node h.pngCDel 2.pngCDel node h.pngCDel 6.pngCDel node.png)
Elements
Vertex figureMonoaugmented rectangular pyramid
Cells12 wedges, 4 triangular prisms, 4 triangular antiprisms, 6 rectangular trapezoprisms
Faces24 isosceles triangles, 8 triangles, 24 isosceles trapezoids, 6+12 rectangles
Edges12+12+24+24
Vertices24
Measures (as derived from unit-edge hexagonal-octagonal duoprism)
Edge lengthsShort edges of rectangles (12): 1
 Side edges (24):
 Edges of triangles (24):
 Long edges of rectangles (12):
Circumradius
Central density1
Euler characteristic0
Related polytopes
ArmyTispap
RegimentTispap
DualTriangular-square tegmantitegmoid
Topological properties
OrientableYes
Properties
Symmetry(B2×G2)/2, order 48
ConvexYes
NatureTame

The triangular-square prismantiprismoid or tispap, also known as the edge-snub triangular-square duoprism or 3-4 prismantiprismoid, is a convex isogonal polychoron that consists of 4 triangular antiprisms, 4 triangular prisms, 6 rectangular trapezoprisms, and 12 wedges. 1 triangular antiprism, 1 triangular prism, 2 rectangular trapezoprisms, and 3 wedges join at each vertex. It can be obtained through the process of alternating one class of edges of the hexagonal-octagonal duoprism so that the octagons become rectangles. 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: ≈ 1:1.57980.

Vertex coordinates[edit | edit source]

The vertices of a triangular-square prismantiprismoid, assuming that the triangular antiprisms are regular and are connected by uniform triangular prisms 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:

Another variant obtained from the uniform hexagonal-octagonal duoprism has coordinates given by: