Decagonal duotruncatoprism

Decagonal duotruncatoprism
(OFF file)
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Dedtep
Elements
Cells	100 tetragonal disphenoids, 200 wedges, 100 rectangular trapezoprisms, 20 didecagonal prisms
Faces	400 isosceles triangles, 400 isosceles trapezoids, 200+200 rectangles, 20 didecagons
Edges	200+200+400+400
Vertices	400
Vertex figure	Mirror-symmetric bi-apiculated tetrahedron
Measures (based on icosagon edge length 1 and same radius ratio as uniform-derived decagonal duoexpandoprism)
Edge lengths	Edges of icosagons (200+200): 1
	Edges of pseudo-decagons (400): $2+{\sqrt {\frac {5+{\sqrt {5}}}{2}}}\approx 3.90211$
	Lacing edges (400): ${\frac {3+{\sqrt {5}}+{\sqrt {10+2{\sqrt {5}}}}}{2}}\approx 4.52015$
Circumradius	${\sqrt {14+5{\sqrt {5}}+5{\sqrt {\frac {25+11{\sqrt {5}}}{2}}}}}\approx 7.07667$
Central density	1
Related polytopes
Army	Dedtep
Regiment	Dedtep
Dual	Decagonal duotruncatotegum
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(10)≀S2, order 800
Convex	Yes
Nature	Tame

The decagonal duotruncatoprism or dedtep is a convex isogonal polychoron and the ninth member of the duotruncatoprism family. It consists of 20 didecagonal prisms, 100 rectangular trapezoprisms, 200 wedges, and 100 tetragonal disphenoids. 2 didecagonal 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 decagonal-didecagonal duoprisms whose didecagonal prisms have a smaller circumradius than their decagonal prisms. However, it cannot be made uniform.