Tortuous tunnel
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Tortuous tunnel  

Rank  3 
Type  Quasiconvex Stewart toroid 
Notation  
Stewart notation  M, Q_{3}Q_{3}/S_{3}S_{3} 
Elements  
Faces  6 squares, 6+6+6 triangles 
Edges  3+3+3+6+12+12 
Vertices  3+6+6 
Measures (edge length 1)  
Volume  
Surface area  
Related polytopes  
Convex hull  Triangular orthobicupola 
Abstract & topological properties  
Flag count  156 
Euler characteristic  0 
Surface  Torus 
Orientable  Yes 
Genus  1 
Properties  
Symmetry  A_{2}×A_{1}, order 12 
Flag orbits  13 
Convex  No 
The tortuous tunnel or M is a quasiconvex Stewart toroid. It can be made by excavating 2 octahedra from a triangular orthobicupola. It has the fewest vertices of any known quasiconvex Stewart toroid, with 15.
Vertex coordinates[edit  edit source]
A tortuous tunnel with edge length 1 has the following vertex coordinates:
 ,
 ,
 ,
 ,
 ,
 .
Gallery[edit  edit source]

A view of the tunnel.
External links[edit  edit source]
 Doskey, Alex. "Chapter 5  Simplest (R)(A)(Q)(T) Toroids of genus p=1".
 McNeil, Jim. "Simple Stewart toroids".
Bibliography[edit  edit source]
 Stewart, Bonnie (1964). Adventures Amoung the Toroids (2 ed.). ISBN 0686119 363.