Decagonal duoprism
Decagonal duoprism  

Rank  4 
Type  Uniform 
Notation  
Bowers style acronym  Dedip 
Coxeter diagram  x10o x10o () 
Elements  
Cells  20 decagonal prisms 
Faces  100 squares, 20 decagons 
Edges  200 
Vertices  100 
Vertex figure  Tetragonal disphenoid, edge lengths √(5+√5)/2 (bases) and √2 (sides) 
Measures (edge length 1)  
Circumradius  
Inradius  
Hypervolume  
Dichoral angles  Dip–10–dip: 144º 
Dip–4–dip: 90°  
Central density  1 
Number of external pieces  20 
Level of complexity  3 
Related polytopes  
Army  Dedip 
Regiment  Dedip 
Dual  Decagonal duotegum 
Conjugate  Decagrammic duoprism 
Abstract & topological properties  
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  I_{2}(10)≀S_{2}, order 800 
Convex  Yes 
Nature  Tame 
The decagonal duoprism or dedip, also known as the decagonaldecagonal duoprism, the 10 duoprism or the 1010 duoprism, is a noble uniform duoprism that consists of 20 decagonal prisms, with four at each vertex. It is also the 209 gyrochoron. It is the first in an infinite family of isogonal decagonal dihedral swirlchora and also the first in an infinite family of isochoric decagonal hosohedral swirlchora.
This polychoron can be alternated into a pentagonal duoantiprism, although it cannot be made uniform.
A unit decagonal duoprism can be edgeinscribed into the small ditetrahedronary hexacosihecatonicosachoron.
Gallery[edit  edit source]

Wireframe, cell, net
Vertex coordinates[edit  edit source]
Coordinates for the vertices of a decagonal duoprism of edge length 1, centered at the origin, are given by:
Representations[edit  edit source]
A decagonal duoprism has the following Coxeter diagrams:
 x10o x10o (full symmetry)
 x5x x10o (one decagon as dipentagon)
 x5x x5x (both decagons have pentagonal symmetry)
External links[edit  edit source]
 Bowers, Jonathan. "Category A: Duoprisms".
 Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".
 Klitzing, Richard. "dadip".
 Wikipedia contributors. "1010 duoprism".