Pentagonal duoprism
Pentagonal duoprism  

Rank  4 
Type  Uniform 
Notation  
Bowers style acronym  Pedip 
Coxeter diagram  x5o x5o () 
Elements  
Cells  10 pentagonal prisms 
Faces  25 squares, 10 pentagons 
Edges  50 
Vertices  25 
Vertex figure  Tetragonal disphenoid, edge lengths (1+√5)/2 (bases) and √2 (sides) 
Measures (edge length 1)  
Circumradius  
Inradius  
Hypervolume  
Dichoral angles  Pip–5–pip: 108° 
Pip–4–pip: 90°  
Central density  1 
Number of external pieces  10 
Level of complexity  3 
Related polytopes  
Army  Pedip 
Regiment  Pedip 
Dual  Pentagonal duotegum 
Conjugate  Pentagrammic duoprism 
Abstract & topological properties  
Flag count  600 
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  H_{2}≀S_{2}, order 200 
Flag orbits  3 
Convex  Yes 
Nature  Tame 
The pentagonal duoprism or pedip, also known as the pentagonalpentagonal duoprism, the 5 duoprism or the 55 duoprism, is a noble uniform duoprism that consists of 10 pentagonal prisms, with 4 meeting at each vertex. It is also the 104 gyrochoron and the square funk prism. It is the first in an infinite family of isogonal pentagonal dihedral swirlchora and also the first in an infinite family of isochoric pentagonal hosohedral swirlchora.
A pentagonal duoprism of edge length 1 contains the vertices of a regular pentachoron of edge length , due to the fact the pentachoron is also the 52 step prism.
Gallery[edit  edit source]

Wireframe, cell, net

Wireframe, cell, net as 104 gyrochoron
Vertex coordinates[edit  edit source]
The vertices of a pentagonal duoprism of edge length 1, centered at the origin, are given by:
 ,
 ,
 ,
 ,
 ,
 ,
 ,
 ,
 .
Representations[edit  edit source]
A pentagonal duoprism has the following Coxeter diagrams:
 x5o x5o () (full symmetry)
 ofx xxx5ooo&#xt (pentagonal axial)
External links[edit  edit source]
 Bowers, Jonathan. "Category A: Duoprisms".
 Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".
 Klitzing, Richard. "pedip".
 Wikipedia contributors. "55 duoprism".