Digonal-pentagonal duoantiprism
Digonal-pentagonal duoantiprism | |
---|---|
File:Digonal-pentagonal duoantiprism.png | |
Rank | 4 |
Type | Isogonal |
Notation | |
Bowers style acronym | Dipdap |
Coxeter diagram | s4o2s10o () |
Elements | |
Cells | 20 digonal disphenoids, 10 tetragonal disphenoids, 4 pentagonal antiprisms |
Faces | 40+40 isosceles triangles, 4 pentagons |
Edges | 10+20+40 |
Vertices | 20 |
Vertex figure | Augmented triangular prism |
Measures (edge length 1) | |
Edge lengths | Lacing (40): |
Digons (10): 1 | |
Edges of pentagons (20): 1 | |
Circumradius | |
Central density | 1 |
Related polytopes | |
Army | Dipdap |
Regiment | Dipdap |
Dual | Digonal-pentagonal duoantitegum |
Abstract & topological properties | |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | (B2×I2(10))/2, order 80 |
Convex | Yes |
Nature | Tame |
The digonal-pentagonal duoantiprism or dipdap, also known as the 2-5 duoantiprism, is a convex isogonal polychoron that consists of 4 pentagonal antiprisms, 10 tetragonal disphenoids, and 20 digonal disphenoids. 2 pentagonal antiprisms, 2 tetragonal disphenoids, and 4 digonal disphenoids join at each vertex. It can be obtained through the process of alternating the square-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: ≈ 1:1.13490.
Vertex coordinates[edit | edit source]
The vertices of a digonal-pentagonal duoantiprism, assuming that the pentagonal antiprisms are uniform of edge length 1, centered at the origin, are given by:
with all even changes of sign except for the first coordinate, and
with all odd changes of sign except for the first coordinate.
An alternate set of coordinates, assuming that the edge length differences are minimized, centered at the origin, are given by:
with all even changes of sign except for the first coordinate, and
with all odd changes of sign except for the first coordinate.