Square-pentagonal duoantiprism
Square-pentagonal duoantiprism | |
---|---|
Rank | 4 |
Type | Isogonal |
Notation | |
Bowers style acronym | Squipdap |
Coxeter diagram | s8o2s10o () |
Elements | |
Cells | 40 digonal disphenoids, 10 square antiprisms, 8 pentagonal antiprisms |
Faces | 80+80 isosceles triangles, 10 squares, 8 pentagons |
Edges | 40+40+80 |
Vertices | 40 |
Vertex figure | Gyrobifastigium |
Measures (based on polygons of edge length 1) | |
Edge lengths | Lacing (80): |
Edges of squares (40): 1 | |
Edges of pentagons (40): 1 | |
Circumradius | |
Central density | 1 |
Related polytopes | |
Army | Squipdap |
Regiment | Squipdap |
Dual | Square-pentagonal duoantitegum |
Abstract & topological properties | |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | (I2(8)×I2(10))/2, order 160 |
Convex | Yes |
Nature | Tame |
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: