Pentagonal-decagrammic duoprism

Pentagonal-decagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Bowers style acronym	Pistadedip
Info
Coxeter diagram	x5o x10/3o
Symmetry	H2×I2(10), order 200
Army	Semi-uniform padedip
Regiment	Pistadedip
Elements
Vertex figure	Digonal disphenoid, edge lengths (1+√5)/2 (base 1), √(5–√5)/2 (base 2), √2 (sides)
Cells	10 pentagonal prisms, 5 decagrammic prisms
Faces	50 squares, 10 pentagons, 5 decagrams
Edges	50+50
Vertices	50
Measures (edge length 1)
Circumradius	√2(5–√5)/5 ≈ 1.05146
Hypervolume	25/8 = 3.125
Dichoral angles	Pip–5–pip: 72°
	Stiddip–10/3–stiddip: 108°
	Pip–4–stiddip: 90°
Central density	3
Related polytopes
Dual	Pentagonal-decagrammic duotegum
Conjugates	Pentagonal-decagonal duoprism, Pentagrammic-decagonal duoprism, Pentagrammic-decagrammic duoprism
Properties
Convex	No
Orientable	Yes
Nature	Tame

The pentagonal-decagrammic duoprism, also known as pistadedip or the 5-10/3 duoprism, is a uniform duoprism that consists of 10 pentagonal prisms and 5 decagrammic prisms, with two of each meeting at each vertex.

Vertex coordinates

The coordinates of a pentagonal-decagrammic duoprism, centered at the origin and with edge length 1, are given by:

• (±1/2, –√(5+2√5)/20, ±1/2, ±√(5–2√5)/2),
• (±1/2, –√(5+2√5)/20, ±(3–√5)/4, ±√(5–√5)/8),
• (±1/2, –√(5+2√5)/20, ±(√5–1)/2, 0),
• (±(1+√5)/4, √(5–√5)/40, ±1/2, ±√(5–2√5)/2),
• (±(1+√5)/4, √(5–√5)/40, ±(3–√5)/4, ±√(5–√5)/8),
• (±(1+√5)/4, √(5–√5)/40, ±(√5–1)/2, 0),
• (0, √(5+√5)/10, ±1/2, ±√(5–2√5)/2),
• (0, √(5+√5)/10, ±(3–√5)/4, ±√(5–√5)/8),
• (0, √(5+√5)/10, ±(√5–1)/2, 0).

External links

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

• Klitzing, Richard. "Pistadedip".