# Pentagonal ditetragoltriate

Pentagonal ditetragoltriate
Rank4
TypeIsogonal
SpaceSpherical
Notation
Bowers style acronymPedet
Elements
Cells25 rectangular trapezoprisms, 10 pentagonal prisms
Faces50 isosceles trapezoids, 50 rectangles, 10 pentagons
Edges25+50+50
Vertices50
Vertex figureNotch
Measures (based on variant with trapezoids with 3 unit edges)
Edge lengthsEdges of smaller pentagon (50): 1
Lacing edges (25): 1
Edges of larger pentagon (50): ${\displaystyle \frac{2+\sqrt{5-\sqrt5}}{2} ≈ 1.83125}$
Circumradius${\displaystyle \sqrt{\frac{15+2\sqrt5+2\sqrt{25+5\sqrt5}}{10}} ≈ 1.77488}$
Central density1
Related polytopes
ArmyPedet
RegimentPedet
DualPentagonal tetrambitriate
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryH2≀S2, order 200
ConvexYes
NatureTame

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:${\displaystyle \frac{2+\sqrt{5-\sqrt5}}{2}}$ ≈ 1:1.83125. This value is also the ratio between the two sides of the two semi-uniform duoprisms.