# Decagonal duotruncatoprism

Decagonal duotruncatoprism
Rank4
TypeIsogonal
Notation
Bowers style acronymDedtep
Elements
Cells100 tetragonal disphenoids, 200 wedges, 100 rectangular trapezoprisms, 20 didecagonal prisms
Faces400 isosceles triangles, 400 isosceles trapezoids, 200+200 rectangles, 20 didecagons
Edges200+200+400+400
Vertices400
Vertex figureMirror-symmetric bi-apiculated tetrahedron
Measures (based on icosagon edge length 1 and same radius ratio as uniform-derived decagonal duoexpandoprism)
Edge lengthsEdges of icosagons (200+200): 1
Edges of pseudo-decagons (400): ${\displaystyle 2+{\sqrt {\frac {5+{\sqrt {5}}}{2}}}\approx 3.90211}$
Lacing edges (400): ${\displaystyle {\frac {3+{\sqrt {5}}+{\sqrt {10+2{\sqrt {5}}}}}{2}}\approx 4.52015}$
Circumradius${\displaystyle {\sqrt {14+5{\sqrt {5}}+5{\sqrt {\frac {25+11{\sqrt {5}}}{2}}}}}\approx 7.07667}$
Central density1
Related polytopes
ArmyDedtep
RegimentDedtep
DualDecagonal duotruncatotegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(10)≀S2, order 800
ConvexYes
NatureTame

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.