Decagonal ditetragoltriate

Decagonal ditetragoltriate
(OFF file)
Rank	4
Type	Isogonal
Space	Spherical
Notation
Bowers style acronym	Dedet
Elements
Cells	100 rectangular trapezoprisms, 20 decagonal prisms
Faces	200 isosceles trapezoids, 200 rectangles, 20 decagons
Edges	100+200+200
Vertices	200
Vertex figure	Notch
Measures (based on variant with trapezoids with 3 unit edges)
Edge lengths	Edges of smaller decagon (200): 1
	Lacing edges (100): 1
	Edges of longer decagon (200): $\frac{4-\sqrt2+\sqrt{10}}{4} \approx 1.43702$
Circumradius	$\sqrt{\frac{7+\sqrt2+2\sqrt5+\sqrt{10}}{2}} \approx 2.83272$
Central density	1
Related polytopes
Army	Dedet
Regiment	Dedet
Dual	Decagonal tetrambitriate
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(10)≀S2, order 800
Convex	Yes
Nature	Tame

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:$\frac{2+\sqrt{3-\sqrt5}}{2}$ ≈ 1:1.43702. This value is also the ratio between the two sides of the two semi-uniform duoprisms.