Pentagonal ditetragoltriate

Pentagonal ditetragoltriate
(OFF file)
Rank	4
Type	Isogonal
Space	Spherical
Notation
Bowers style acronym	Pedet
Elements
Cells	25 rectangular trapezoprisms, 10 pentagonal prisms
Faces	50 isosceles trapezoids, 50 rectangles, 10 pentagons
Edges	25+50+50
Vertices	50
Vertex figure	Notch
Measures (based on variant with trapezoids with 3 unit edges)
Edge lengths	Edges of smaller pentagon (50): 1
	Lacing edges (25): 1
	Edges of larger pentagon (50): $\frac{2+\sqrt{5-\sqrt5}}{2} ≈ 1.83125$
Circumradius	$\sqrt{\frac{15+2\sqrt5+2\sqrt{25+5\sqrt5}}{10}} ≈ 1.77488$
Central density	1
Related polytopes
Army	Pedet
Regiment	Pedet
Dual	Pentagonal tetrambitriate
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H2≀S2, order 200
Convex	Yes
Nature	Tame

The pentagonal ditetragoltriate or pedet is a convex isogonal polychoron and the third member of the ditetragoltriate family. It consists of 10 pentagonal prisms and 25 rectangular trapezoprisms. 2 pentagonal 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 pentagonal prismatic swirlchora.

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

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$\frac{2+\sqrt{5-\sqrt5}}{2}$ ≈ 1:1.83125. This value is also the ratio between the two sides of the two semi-uniform duoprisms.