Pentagonal triswirlprism

Pentagonal triswirlprism
(OFF file)
Rank	4
Type	Isogonal
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): ${\sqrt {\frac {15+{\sqrt {5}}-{\sqrt {150+30{\sqrt {5}}}}}{10}}}\approx 0.50024$
	Long side edges (150): ${\sqrt {\frac {35+7{\sqrt {5}}-{\sqrt {750+330{\sqrt {5}}}}}{20}}}\approx 0.77715$
	Edges of pentagons (150): 1
Circumradius	${\sqrt {\frac {5+{\sqrt {5}}}{5}}}\approx 1.20300$
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:${\frac {\sqrt {30+2{\sqrt {5}}+2{\sqrt {150+30{\sqrt {5}}}}}}{4}}$ ≈ 1:1.99906.