# 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): ${\displaystyle {\frac {\sqrt {30}}{6}}\approx 0.91287}$
Digons (6): 1
Edges of triangles (12): 1
Circumradius${\displaystyle {\frac {\sqrt {21}}{6}}\approx 0.76376}$
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:${\displaystyle {\frac {\sqrt {30}}{5}}}$ ≈ 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

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:

• ${\displaystyle \left(0,\,{\frac {\sqrt {3}}{3}},\,{\frac {\sqrt {6}}{6}},\,{\frac {\sqrt {6}}{6}}\right),}$

with all even changes of sign, and

• ${\displaystyle \left(\pm {\frac {1}{2}},\,{\frac {\sqrt {3}}{6}},\,{\frac {\sqrt {6}}{6}},\,{\frac {\sqrt {6}}{6}}\right),}$

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:

• ${\displaystyle \left(0,\,{\frac {\sqrt {3}}{3}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}}\right),}$

with all even changes of sign, and

• ${\displaystyle \left(\pm {\frac {1}{2}},\,{\frac {\sqrt {3}}{6}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}}\right).}$

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