Pentagonal duotruncatoprism

Pentagonal duotruncatoprism
(OFF file)
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Pedtep
Elements
Cells	25 tetragonal disphenoids, 50 wedges, 25 rectangular trapezoprisms, 10 dipentagonal prisms
Faces	100 isosceles triangles, 100 isosceles trapezoids, 50+50 rectangles, 10 dipentagons
Edges	50+50+100+100
Vertices	100
Vertex figure	Mirror-symmetric bi-apiculated tetrahedron
Measures (based on decagon edge length 1 and same radius ratio as uniform-derived pentagonal duoexpandoprism)
Edge lengths	Edges of decagons (50+50): 1
	Lacing edges (100): ${\frac {{\sqrt {2}}+{\sqrt {10}}}{2}}\approx 2.28825$
	Edges of pseudo-pentagons (100): ${\frac {5+{\sqrt {5}}}{2}}\approx 3.61803$
Circumradius	${\sqrt {\frac {13+5{\sqrt {5}}}{2}}}\approx 3.47709$
Central density	1
Related polytopes
Army	Pedtep
Regiment	Pedtep
Dual	Pentagonal duotruncatotegum
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H2≀S2, order 200
Convex	Yes
Nature	Tame

The pentagonal duotruncatoprism or pedtep is a convex isogonal polychoron and the fourth member of the duoexpandoprism family. It consists of 10 dipentagonal prisms, 25 rectangular trapezoprisms, 50 wedges, and 25 tetragonal disphenoids. 2 dipentagonal prisms, 2 rectangular trapezoprisms, 3 wedges, and 1 tetragonal disphenoid join at each vertex. It can be obtained as the convex hull of two orthogonal semi-uniform pentagonal-dipentagonal duoprisms whose dipentagonal prism cells have a smaller coircumradius than the pentagonal prisms. However, it cannot be made uniform.