Small biprismatorhombatodecachoron

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Small biprismatorhombatodecachoron
Rank4
TypeIsogonal
Notation
Bowers style acronymSabipard
Coxeter diagramac3bo3ob3ca&#zd (c < a+b/3)
Elements
Cells20 triangular prisms, 60 wedges, 20 triangular antiprisms, 30 rectangular trapezoprisms, 10 rhombitetratetrahedra
Faces40+40 triangles, 120 isosceles triangles, 60+60 rectangles, 120 isosceles trapezoids
Edges60+120+120+120
Vertices120
Vertex figureTriangular-rectangular wedge
Measures (based on two prismatorhombated pentachora of edge length 1)
Edge lengthsLacing edges (120):
 Remaining edges (60+120+120): 1
Circumradius
Central density1
Related polytopes
ArmySabipard
RegimentSabipard
DualSmall bicrystallorthodecachoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryA4×2, order 240
ConvexYes
NatureTame

The small biprismatorhombatodecachoron or sabipard is a convex isogonal polychoron that consists of 10 rhombitetratetrahedra, 30 rectangular trapezoprisms, 20 triangular prisms, 20 triangular antiprisms, and 60 wedges. 1 rhombitetratetrahedron, 2 rectangular trapezoprisms, 1 triangular prism, 1 triangular antiprism, and 3 wedges join at each vertex.

It is one of a total of five distinct polychora (including two transitional cases) that can be obtained as the convex hull of two opposite prismatorhombated pentachora. In this case, if the prismatorhombated pentachora are of the form a3b3o3c, then c must be less than a+b/3 (producing the transitional biprismatorhombatodecachoron in the limiting case). This includes the convex hull of two uniform prismatorhombated pentachora. The lacing edges generally have length .

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.35389.

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