Digonal-pentagonal duoantiprism

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Digonal-pentagonal duoantiprism
File:Digonal-pentagonal duoantiprism.png
Rank4
TypeIsogonal
Notation
Bowers style acronymDipdap
Coxeter diagrams4o2s10o ()
Elements
Cells20 digonal disphenoids, 10 tetragonal disphenoids, 4 pentagonal antiprisms
Faces40+40 isosceles triangles, 4 pentagons
Edges10+20+40
Vertices20
Vertex figureAugmented triangular prism
Measures (edge length 1)
Edge lengthsLacing (40):
 Digons (10): 1
 Edges of pentagons (20): 1
Circumradius
Central density1
Related polytopes
ArmyDipdap
RegimentDipdap
DualDigonal-pentagonal duoantitegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
Symmetry(B2×I2(10))/2, order 80
ConvexYes
NatureTame

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.