Hexagonal duotegum

Hexagonal duotegum
(OFF file)
Rank	4
Type	Noble
Notation
Bowers style acronym	Hiddit
Coxeter diagram	m6o2m6o ()
Elements
Cells	36 tetragonal disphenoids
Faces	72 isosceles triangles
Edges	12+36
Vertices	12
Vertex figure	Hexagonal tegum
Measures (based on hexagons of edge length 1)
Edge lengths	Base (12): 1
	Lacing (36): ${\sqrt {2}}\approx 1.41421$
Circumradius	1
Inradius	${\frac {\sqrt {6}}{4}}\approx 0.61237$
Central density	1
Related polytopes
Army	Hiddit
Regiment	Hiddit
Dual	Hexagonal duoprism
Conjugate	None
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	G2≀S2, order 288
Convex	Yes
Nature	Tame

"12-5 step prism" redirects here. For its vertex coordinates, see Dodecagonal-dodecagrammic coil.

The hexagonal duotegum or hiddit, also known as the hexagonal-hexagonal duotegum, the 6 duotegum, or the 6-6 duotegum, is a noble duotegum that consists of 36 tetragonal disphenoids and 12 vertices, with 12 cells joining at each vertex. It is also the 12-5 step prism. It is the first in an infinite family of isogonal hexagonal hosohedral swirlchora and also the first in an infinite family of isochoric hexagonal dihedral swirlchora.

The ratio between the longest and shortest edges is 1:${\sqrt {2}}$ ≈ 1:1.41421.

Vertex coordinates

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

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