Digonal-triangular duoantiprism

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Digonal-triangular duoantiprism
File:Digonal-triangular duoantiprism.png
Rank4
TypeIsogonal
Notation
Bowers style acronymDitdap
Coxeter diagrams4o2s6o ()
Elements
Cells12 digonal disphenoids, 6 tetragonal disphenoids, 4 triangular antiprisms
Faces24+24 isosceles triangles, 4 triangles
Edges6+12+24
Vertices12
Vertex figureAugmented triangular prism
Measures (based on component polygons of edge length 1)
Edge lengthsLacing edges (24):
 Digons (6): 1
 Edges of triangles (12): 1
Circumradius
Central density1
Related polytopes
ArmyDitdap
RegimentDitdap
DualDigonal-triangular duoantitegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
Symmetry(B2×G2)/2, order 48
ConvexYes
NatureTame

The digonal-triangular duoantiprism or ditdap, also known as the 2-3 duoantiprism, is a convex isogonal polychoron that consists of 4 triangular antiprisms, 6 tetragonal disphenoids, and 12 digonal disphenoids. 2 triangular antiprisms, 2 tetragonal disphenoids, and 4 digonal disphenoids join at each vertex. It can be obtained through the process of alternating the square-hexagonal 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: ≈ 1:1.09545. In this specific variant the digonal disphenoids become tetragonal disphenoids. A variant where the triangular antiprisms become fully regular octahedra also exists.

Vertex coordinates[edit | edit source]

The vertices of a digonal-triangular duoantiprism, assuming that the triangular antiprisms are regular octahedra of edge length 1, centered at the origin, are given by:

with all even changes of sign, and

with all odd changes of sign except for the first coordinate.

An alternate set of coordinates where the digonal disphenoids become tetragonal disphenoids, centered at the origin, are given by:

with all even changes of sign, and

with all odd changes of sign except for the first coordinate.


External links[edit | edit source]