Pentagonal triswirlprism

Pentagonal triswirlprism
(OFF file)
Rank	4
Type	Isogonal
Space	Spherical
Elements
Cells	150 phyllic disphenoids, 30 pentagonal gyroprisms
Faces	300 scalene triangles, 150 isosceles triangles, 30 pentagons
Edges	75+150+150
Vertices	75
Vertex figure	10-vertex polyhedron with 4 tetragons and 8 triangles
Measures (based on pentagonal duoprisms of edge length 1)
Edge lengths	Short side edges (75): $\sqrt{\frac{15+\sqrt5-\sqrt{150+30\sqrt5}}{10}} ≈ 0.50024$
	Long side edges (150): $\sqrt{\frac{35+7\sqrt5-\sqrt{750+330\sqrt5}}{20}} ≈ 0.77715$
	Edges of pentagons (150): 1
Circumradius	$\sqrt{\frac{5+\sqrt5}{5}} ≈ 1.20300$
Central density	1
Related polytopes
Dual	Pentagonal triswirltegum
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	(I2(15)≀S2)+/3, order 300
Convex	Yes
Nature	Tame

The pentagonal triswirlprism is a convex isogonal polychoron and member of the duoprismatic swirlprism family that consists of 30 pentagonal gyroprisms and 150 phyllic disphenoids. 4 pentagonal gyroprisms and 8 phyllic disphenoids join at each vertex. It can be obtained as a subsymmetrical faceting of the pentadecagonal duoprism. It is the third in an infinite family of isogonal pentagonal dihedral swirlchora.

The ratio between the longest and shortest edges is 1:$\frac{\sqrt{30+2\sqrt5+2\sqrt{150+30\sqrt5}}}{4}$ ≈ 1:1.99906.