# Truncated pentagonal duoprism

Truncated pentagonal duoprism
Rank4
TypeIsogonal
Notation
Bowers style acronymTapedip
Elements
Cells25 tetragonal disphenoids, 10 truncated pentagonal prisms
Faces100 isosceles triangles, 25 ditetragons, 10 dipentagons
Edges50+50+100
Vertices100
Vertex figureSphenoid
Measures (variant with decagon edge length 1)
Edge lengthsLacing edges (100): ${\displaystyle {\frac {{\sqrt {10}}-{\sqrt {2}}}{2}}\approx 0.87403}$
Edges of decagons (50+50): 1
Circumradius${\displaystyle {\sqrt {4+{\sqrt {5}}}}\approx 2.49721}$
Central density1
Related polytopes
ArmyTapedip
RegimentTapedip
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryH2≀S2, order 200
ConvexYes
NatureTame

The truncated pentagonal duoprism or tapedip is a convex isogonal polychoron that consists of 10 truncated pentagonal prisms and 25 tetragonal disphenoids. 1 tetragonal disphenoid and 3 truncated pentagonal prisms join at each vertex. It can be formed by truncating the pentagonal duoprism.

It can also be obtained as the convex hull of 2 semi-uniform pentagonal-decagonal duoprisms chosen such that the decagonal and pentagonal prisms have the same circumradius. if the decagons of this duoprism have edge length 1, the pentagons have edge length ${\displaystyle {\sqrt {5}}\approx 2.23607}$.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:${\displaystyle {\frac {\sqrt {3+{\sqrt {5}}}}{2}}\approx 1.14412}$.