# Decagonal ditetragoltriate

Decagonal ditetragoltriate
Rank4
TypeIsogonal
SpaceSpherical
Notation
Bowers style acronymDedet
Elements
Cells100 rectangular trapezoprisms, 20 decagonal prisms
Faces200 isosceles trapezoids, 200 rectangles, 20 decagons
Edges100+200+200
Vertices200
Vertex figureNotch
Measures (based on variant with trapezoids with 3 unit edges)
Edge lengthsEdges of smaller decagon (200): 1
Lacing edges (100): 1
Edges of longer decagon (200): ${\displaystyle \frac{4-\sqrt2+\sqrt{10}}{4} \approx 1.43702}$
Circumradius${\displaystyle \sqrt{\frac{7+\sqrt2+2\sqrt5+\sqrt{10}}{2}} \approx 2.83272}$
Central density1
Related polytopes
ArmyDedet
RegimentDedet
DualDecagonal tetrambitriate
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(10)≀S2, order 800
ConvexYes
NatureTame

The decagonal ditetragoltriate or dedet is a convex isogonal polychoron and the eighth member of the ditetragoltriate family. It consists of 20 decagonal prisms and 100 rectangular trapezoprisms. 2 decagonal prisms and 4 rectangular trapezoprisms join at each vertex. However, it cannot be made uniform. It is the first in an infinite family of isogonal decagonal prismatic swirlchora.

This polychoron can be alternated into the grand antiprism, which can be made uniform.

It can be obtained as the convex hull of 2 similarly oriented semi-uniform decagonal duoprisms, one with a larger xy decagon and the other with a larger zw decagon.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:${\displaystyle \frac{2+\sqrt{3-\sqrt5}}{2}}$ ≈ 1:1.43702. This value is also the ratio between the two sides of the two semi-uniform duoprisms.