Pentagonal-snub cubic duoantiprism

Pentagonal-snub cubic duoantiprism
File:Pentagonal-snub cubic duoantiprism.png (OFF file)
Rank	5
Type	Isogonal
Notation
Bowers style acronym	Pesnicdap
Coxeter diagram	s10o2s4s3s
Elements
Tera	240 sphenoidal pyramids, 12 digonal-pentagonal duoantiprisms, 8 triangular-pentagonal duoantiprisms, 6 square-pentagonal duoantiprisms, 10 snub cubic antiprisms
Cells	480 irregular tetrahedra, 240+240+240 sphenoids, 120 rhombic disphenoids, 80 triangular gyroprisms, 60 square gyroprisms, 24+24+24 pentagonal antiprisms, 10 snub cubes
Faces	480+480+480 scalene triangles, 240+240+240+240 isosceles triangles, 80 triangles, 60 squares, 48 pentagons
Edges	120+240+240+240+240+240+240
Vertices	240
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Pentagonal-pentagonal icositetrahedral duoantitegum
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	(I2(10)×B3)+, order 480
Convex	Yes
Nature	Tame

The pentagonal-snub cubic duoantiprism, or pesnicdap, is a convex isogonal polyteron that consists of 10 snub cubic antiprisms, 6 square-pentagonal duoantiprisms, 8 triangular-pentagonal duoantiprisms, 12 digonal-pentagonal duoantiprisms, and 240 sphenoidal pyramids. 2 snub cubic antiprisms, 1 square-pentagonal duoantiprism, 1 triangular-pentagonal duoantiprism, 1 digonal-pentagonal duoantiprism, and 5 sphenoidal pyramids join at each vertex. It can be obtained through the process of alternating the decagonal-great rhombicuboctahedral duoprism. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:${\sqrt {\frac {85+30{\sqrt {2}}+{\sqrt {655+450{\sqrt {2}}}}}{93}}}$ ≈ 1:1.32536.