Digonal-triangular duoantiprism

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.

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

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

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

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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