Triangular-pentagonal duoprism

Triangular-pentagonal duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Trapedip
Coxeter diagram	x3o x5o ()
Elements
Cells	5 triangular prisms, 3 pentagonal prisms
Faces	5 triangles, 15 squares, 3 pentagons
Edges	15+15
Vertices	15
Vertex figure	Digonal disphenoid, edge lengths 1 (base 1), (1+√5)/2 (base 2), and √2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {25+3{\sqrt {5}}}{30}}}\approx 1.02808$
Hypervolume	${\frac {\sqrt {75+30{\sqrt {5}}}}{16}}\approx 0.74499$
Dichoral angles	Trip–3–trip: 108°
	Trip–4–pip: 90°
	Pip–5–pip: 60°
Height	${\frac {\sqrt {3}}{2}}\approx 0.86603$
Central density	1
Number of external pieces	8
Level of complexity	6
Related polytopes
Army	Trapedip
Regiment	Trapedip
Dual	Triangular-pentagonal duotegum
Conjugate	Triangular-pentagrammic duoprism
Abstract & topological properties
Flag count	360
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A2×H2, order 60
Flag orbits	6
Convex	Yes
Nature	Tame

The triangular-pentagonal duoprism, also known as the 3-5 duoprism, is a uniform duoprism that consists of 3 pentagonal prisms and 5 triangular prisms, with two of each at each vertex.

It is also a CRF segmentochoron, as pentagon atop pentagonal prism. It is designated K-4.34 on Richard Klitzing's list.

Gallery

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  Net

Vertex coordinates

Coordinates for the vertices of a triangular-pentagonal duoprism with edge length 1 are given by:

• $\left(0,\,{\frac {\sqrt {3}}{3}},\,0,\,{\sqrt {\frac {5+{\sqrt {5}}}{10}}}\right)$,
• $\left(0,\,{\frac {\sqrt {3}}{3}},\,\pm {\frac {1+{\sqrt {5}}}{4}},\,{\sqrt {\frac {5-{\sqrt {5}}}{40}}}\right)$,
• $\left(0,\,{\frac {\sqrt {3}}{3}},\,\pm {\frac {1}{2}},\,-{\sqrt {\frac {5+2{\sqrt {5}}}{20}}}\right)$,
• $\left(\pm {\frac {1}{2}},\,-{\frac {\sqrt {3}}{6}},\,0,\,{\sqrt {\frac {5+{\sqrt {5}}}{10}}}\right)$,
• $\left(\pm {\frac {1}{2}},\,-{\frac {\sqrt {3}}{6}},\,\pm {\frac {1+{\sqrt {5}}}{4}},\,{\sqrt {\frac {5-{\sqrt {5}}}{40}}}\right)$,
• $\left(\pm {\frac {1}{2}},\,-{\frac {\sqrt {3}}{6}},\,\pm {\frac {1}{2}},\,-{\sqrt {\frac {5+2{\sqrt {5}}}{20}}}\right)$.

Representations

A triangular-pentagonal duoprism has the following Coxeter diagrams:

• x3o x5o () (full symmetry)
• ox xx5oo&#x (pentagon atop pentagon prism)
• ofx xxx3oooo&#xt (triangle-first)

External links

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

• Klitzing, Richard. "trapedip".
• Wikipedia contributors. "3-5 duoprism".