# Truncated decagonal duoprism

Truncated decagonal duoprism
Rank4
TypeIsogonal
SpaceSpherical
Notation
Elements
Cells100 tetragonal disphenoids, 20 truncated decagonal prisms
Faces400 isosceles triangles, 100 ditetragons, 20 didecagons
Edges200+200+400
Vertices400
Vertex figureSphenoid
Measures (variant with icosagon edge length 1)
Edge lengthsLacing edges (400): $\sqrt{\frac{5-\sqrt5}{5}} ≈ 0.74350$ Edges of icosagons (200+200): 1
Circumradius$\sqrt{\frac{65+19\sqrt5+\sqrt{5650+2390\sqrt5}}{10}} ≈ 4.60802$ Central density1
Related polytopes
DualTetrakis decagonal duotegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(10)≀S2, order 800
ConvexYes
NatureTame

The truncated decagonal duoprism or tadedip is a convex isogonal polychoron that consists of 20 truncated decagonal prisms and 100 tetragonal disphenoids. 1 tetragonal disphenoid and 3 truncated decagonal prisms join at each vertex. It can be formed by truncating the decagonal duoprism.

It can also be obtained as the convex hull of 2 semi-uniform decagonal-icosagonal duoprisms chosen such that the icosagonal and decagonal prisms have the same circumradius. if the icosagons of this duoprism have edge length 1, the decagons have edge length $1+\sqrt{\frac{10-2\sqrt5}{5}} ≈ 2.05136$ .

Using the ratio method, the lowest poossible ratio between the longest and shortest edges is 1:$\frac{\sqrt{5+\sqrt5}}{2}$ ≈ 1:1.34500.