Triangular-dodecagonal duoprism

Triangular-dodecagonal duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Titwadip
Coxeter diagram	x3o x12o ()
Elements
Cells	12 triangular prisms, 3 dodecagonal prisms
Faces	12 triangles, 36 squares, 3 dodecagons
Edges	36+36
Vertices	36
Vertex figure	Digonal disphenoid, edge lengths 1 (base 1), (√2+√6)/2 (base 2), and √2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {7+3{\sqrt {3}}}{3}}}\approx 2.01628$
Hypervolume	${\frac {3(3+2{\sqrt {3}})}{4}}\approx 4.84808$
Dichoral angles	Trip–3–trip: 150°
	Trip–4–twip: 90°
	Twip–12–twip: 60°
Height	${\frac {\sqrt {3}}{2}}\approx 0.86603$
Central density	1
Number of external pieces	15
Level of complexity	6
Related polytopes
Army	Titwadip
Regiment	Titwadip
Dual	Triangular-dodecagonal duotegum
Conjugate	Triangular-dodecagrammic duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A2×I2(12), order 144
Convex	Yes
Nature	Tame

The triangular-dodecagonal duoprism or titwadip, also known as the 3-12 duoprism, is a uniform duoprism that consists of 3 dodecagonal prisms and 12 triangular prisms, with two of each joining at each vertex. It can also be seen as a convex segmentochoron, being a dodecagon atop a dodecagonal prism.

This polychoron can be subsymmetrically faceted into a 12-4 step prism, although it cannot be made uniform.

Vertex coordinates

The vertices of a triangular-dodecagonal duoprism of edge length 1, centered at the origin, are given by:

• $\left(0,\,{\frac {\sqrt {3}}{3}},\,\pm {\frac {1+{\sqrt {3}}}{2}},\,\pm {\frac {1+{\sqrt {3}}}{2}}\right),$
• $\left(\pm {\frac {1}{2}},\,-{\frac {\sqrt {3}}{6}},\,\pm {\frac {1+{\sqrt {3}}}{2}},\,\pm {\frac {1+{\sqrt {3}}}{2}}\right),$
• $\left(0,\,{\frac {\sqrt {3}}{3}},\,\pm {\frac {1}{2}},\,\pm {\frac {2+{\sqrt {3}}}{2}}\right),$
• $\left(\pm {\frac {1}{2}},\,-{\frac {\sqrt {3}}{6}},\,\pm {\frac {1}{2}},\,\pm {\frac {2+{\sqrt {3}}}{2}}\right),$
• $\left(0,\,{\frac {\sqrt {3}}{3}},\,\pm {\frac {2+{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}}\right),$
• $\left(\pm {\frac {1}{2}},\,-{\frac {\sqrt {3}}{6}},\,\pm {\frac {2+{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}}\right).$

External links

• Bowers, Jonathan. "Category A: Duoprisms".

• Klitzing, Richard. "titwadip".