# Pentagonal duotruncatoprism

Pentagonal duotruncatoprism
Rank4
TypeIsogonal
SpaceSpherical
Notation
Bowers style acronymPedtep
Elements
Cells25 tetragonal disphenoids, 50 wedges, 25 rectangular trapezoprisms, 10 dipentagonal prisms
Faces100 isosceles triangles, 100 isosceles trapezoids, 50+50 rectangles, 10 dipentagons
Edges50+50+100+100
Vertices100
Vertex figureMirror-symmetric bi-apiculated tetrahedron
Measures (based on decagon edge length 1 and same radius ratio as uniform-derived pentagonal duoexpandoprism)
Edge lengthsEdges of decagons (50+50): 1
Lacing edges (100): ${\displaystyle \frac{\sqrt2+\sqrt{10}}{2} ≈ 2.28825}$
Edges of pseudo-pentagons (100): ${\displaystyle \frac{5+\sqrt5}{2} ≈ 3.61803}$
Circumradius${\displaystyle \sqrt{\frac{13+5\sqrt5}{2}} ≈ 3.47709}$
Central density1
Related polytopes
ArmyPedtep
RegimentPedtep
DualPentagonal duotruncatotegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryH2≀S2, order 200
ConvexYes
NatureTame

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.