Pentagonal-snub dodecahedral duoprism

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Pentagonal-snub dodecahedral duoprism
Rank5
TypeUniform
Notation
Bowers style acronymPesnid
Coxeter diagramx5o s5s3s ()
Elements
Tera20+60 triangular-pentagonal duoprisms, 12 pentagonal duoprisms, 5 snub dodecahedral prisms
Cells100+300 triangular prisms, 30+60+60+60 pentagonal prisms, 5 snub dodecahedra
Faces100+300 triangles, 150+300+300 squares, 60+60 pentagons
Edges150+300+300+300
Vertices300
Vertex figureMirror-symmetric pentagonal scalene, edge lengths 1, 1, 1, 1, (1+5)/2 (base pentagon), (1+5)/2 (top edge), 2 (side edges)
Measures (edge length 1)
Circumradius≈ 2.31759
Hypervolume≈ 64.71860
Diteral anglesTrapedip–pip–trapedip: ≈ 164.17537°
 Trapedip–pip–pedip: ≈ 152.92992°
 Sniddip–snid–sniddip: 108°
 Trapedip–trip–sniddip: 90°
 Pedip–pip–sniddip: 90°
Central density1
Number of external pieces97
Level of complexity50
Related polytopes
ArmyPesnid
RegimentPesnid
DualPentagonal-pentagonal hexecontahedral duotegum
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryH3+×H2+, order 600
ConvexYes
NatureTame

The pentagonal-snub dodecahedral duoprism or pesnid is a convex uniform duoprism that consists of 5 snub dodecahedral prisms, 12 pentagonal duoprisms, and 80 triangular-pentagonal duoprisms of two kinds. Each vertex joins 2 snub dodecahedral prisms, 4 triangular-pentagonal duoprisms, and 1 pentagonal duoprism.

Vertex coordinates[edit | edit source]

The vertices of a pentagonal-snub dodecahedral duoprism of edge length 1 are given by all even permutations with an odd number of sign changes of the last three coordinates of:

as well as all even permutations with an even number of sign changes of the last three coordinates of:

where