72 gyrochoron
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72 gyrochoron  

Rank  4 
Type  Isotopic 
Elements  
Cells  7 bilaterallysymmetric edgetruncated tetrahedra 
Faces  7 isosceles triangles, 7 kites, 7 mirrorsymmetric pentagons 
Edges  7+7+14 
Vertices  7+7 
Vertex figure  7+7 phyllic disphenoids 
Measures (edge length 1)  
Central density  1 
Related polytopes  
Dual  72 step prism 
Abstract & topological properties  
Flag count  336 
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  S_{2}(I_{2}(7)2), order 14 
Flag orbits  24 
Convex  Yes 
Nature  Tame 
The 72 gyrochoron, also known as mÃ¶bius 7, is a convex isotopic polychoron and member of the gyrochoron family with 7 bilaterallysymmetric edgetruncated tetrahedra as cells. It is the simplest gyrochoron after the pentachoron and triangular duoprism, both members of existing families, as well as the only isochoric polychoron with 7 cells. It can also be constructed as the 73 gyrochoron. It is also the triangular funk prism.
Each cell of this polychoron has bilateral symmetry, with 2 mirrorsymmetric pentagons, 2 kites, and 2 isosceles triangles for faces, and shares a face with every other cell.
Gallery[edit  edit source]

Wireframe, cell, net
Isogonal derivatives[edit  edit source]
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 Edgetruncated tetrahedron (7): 72 step prism
 Mirrorsymmetric pentagon (7): 72 step prism
 Kite (7): 72 step prism
 Isosceles triangle (7): 72 step prism
 Edge (7): 72 step prism
 Edge (14): 142 step prism
 Vertex (7): 72 step prism
External links[edit  edit source]
 Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".