# Hexagonal duoantiprism

Hexagonal duoantiprism
Rank4
TypeIsogonal
Notation
Bowers style acronymHiddap
Coxeter diagrams12o2s12o ()
Elements
Cells72 tetragonal disphenoids, 24 hexagonal antiprisms
Faces288 isosceles triangles, 24 hexagons
Edges144+144
Vertices72
Vertex figureGyrobifastigium
Measures (based on hexagons of edge length 1)
Edge lengthsLacing (144): ${\displaystyle {\sqrt {3}}-1\approx 0.73205}$
Edges of hexagons (144): 1
Circumradius${\displaystyle {\sqrt {2}}\approx 1.41421}$
Central density1
Related polytopes
ArmyHiddap
RegimentHiddap
DualHexagonal duoantitegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
Symmetry(I2(12)≀S2)/2, order 576
ConvexYes
NatureTame

The hexagonal duoantiprism or hiddap, also known as the hexagonal-hexagonal duoantiprism, the 6 duoantiprism or the 6-6 duoantiprism, is a convex isogonal polychoron that consists of 24 hexagonal antiprisms and 72 tetragonal disphenoids. 4 hexagonal antiprisms and 4 tetragonal disphenoids join at each vertex. It can be obtained through the process of alternating the dodecagonal duoprism. However, it cannot be made uniform, and has two edge lengths. It is the second in an infinite family of isogonal hexagonal dihedral swirlchora.

The ratio between the longest and shortest edges is 1:${\displaystyle {\frac {1+{\sqrt {3}}}{2}}}$ ≈ 1:1.36603.

## Vertex coordinates

The vertices of a hexagonal duoantiprism based on hexagons of edge length 1, centered at the origin, are given by:

• ${\displaystyle \left(\pm 1,\,0,\,\pm 1,\,0\right),}$
• ${\displaystyle \left(\pm 1,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}},\,\pm 1,\,0\right),}$
• ${\displaystyle \left(+{\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}}\right),}$
• ${\displaystyle \left(0,\,\pm 1,\,0,\,\pm 1\right),}$
• ${\displaystyle \left(0,\,\pm 1,\,\pm {\frac {\sqrt {3}}{2}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {\sqrt {3}}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm 1\right),}$
• ${\displaystyle \left(\pm {\frac {\sqrt {3}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}},\,\pm {\frac {1}{2}}\right).}$