Square-pentagonal duoantiprism

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Square-pentagonal duoantiprism
Rank4
TypeIsogonal
Notation
Bowers style acronymSquipdap
Coxeter diagrams8o2s10o ()
Elements
Cells40 digonal disphenoids, 10 square antiprisms, 8 pentagonal antiprisms
Faces80+80 isosceles triangles, 10 squares, 8 pentagons
Edges40+40+80
Vertices40
Vertex figureGyrobifastigium
Measures (based on polygons of edge length 1)
Edge lengthsLacing (80):
 Edges of squares (40): 1
 Edges of pentagons (40): 1
Circumradius
Central density1
Related polytopes
ArmySquipdap
RegimentSquipdap
DualSquare-pentagonal duoantitegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
Symmetry(I2(8)×I2(10))/2, order 160
ConvexYes
NatureTame

The square-pentagonal duoantiprism or squipdap, also known as the 4-5 duoantiprism, is a convex isogonal polychoron that consists of 8 pentagonal antiprisms, 10 square antiprisms, and 40 digonal disphenoids. 2 pentagonal antiprisms, 2 square antiprisms, and 4 digonal disphenoids join at each vertex. It can be obtained through the process of alternating the octagonal-decagonal duoprism. However, it cannot be made uniform, as it generally has 3 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: ≈ 1:1.32536.

Vertex coordinates[edit | edit source]

The vertices of a square-pentagonal duoantiprism based on squares and pentagons of edge length 1, centered at the origin, are given by: