Pentagonal antiditetragoltriate

Pentagonal antiditetragoltriate
(OFF file)
Rank	4
Type	Isogonal
Space	Spherical
Notation
Bowers style acronym	Paddet
Elements
Cells	25+25 tetragonal disphenoids, 50 rectangular pyramids, 10 pentagonal prisms
Faces	100+100 isosceles triangles, 50 rectangles, 10 pentagons
Edges	50+50+100
Vertices	50
Vertex figure	Biaugmented triangular prism
Measures (based on same duoprisms as optimized pentagonal ditetragoltriate)
Edge lengths	Edges of smaller pentagon (50): 1
	Lacing edges (50): $\sqrt{\frac{10-\sqrt5+\sqrt{50+20\sqrt5}}{5}} ≈ 1.41855$
	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	Paddet
Regiment	Paddet
Dual	Pentagonal antitetrambitriate
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	h2≀S2, order 200
Convex	Yes
Nature	Tame

The pentagonal antiditetragoltriate or paddet is a convex isogonal polychoron and the third member of the antiditetragoltriate family. It consists of 10 pentagonal prisms, 50 rectangular pyramids, and 50 tetragonal disphenoids of two kinds. 2 pentagonal prisms, 4 tetragonal disphenoids, and 5 rectangular pyramids join at each vertex. However, it cannot be made scaliform.

It can be formed as the convex hull of 2 oppositely oriented semi-uniform pentagonal duoprisms where the larger pentagon is more than $\sqrt5-1$ times the edge length of the smaller one.

The grand antiprism can be thought of as the convex hull of two inversely oriented pentagonal antiditetragoltriates, with the pentagons having a ratio of 1:$\frac{1+\sqrt5}{2}$ ≈ 1:1.61803.