Cake pan
(Redirected from Tunnelled elongated triangular cupola)
Cake pan  

Rank  3 
Type  Quasiconvex Stewart toroid 
Notation  
Stewart notation  Q_{3}P_{6}/P_{3}Q_{3} 
Elements  
Faces  3+3+3+3+3 squares, 3+3 triangles 
Edges  3+3+3+3+3+3+3+6+6+6 
Vertices  3+3+6+6 
Measures (edge length 1)  
Volume  
Surface area  
Related polytopes  
Convex hull  Elongated triangular cupola 
Abstract & topological properties  
Flag count  156 
Euler characteristic  0 
Surface  Torus 
Orientable  Yes 
Genus  1 
Properties  
Symmetry  A_{2}×I, order 6 
Flag orbits  26 
Convex  No 
The cake pan is a quasiconvex Stewart toroid. It is a tunnelling of a elongated triangular cupola by a triangular cupola and a triangular prism.
It has 21 faces, the fewest faces of any known Stewart toroid.
Vertex coordinates[edit  edit source]
A cake pan with edge length 1 has the following vertex coordinates:
 ,
 ,
 ,
 .
Gallery[edit  edit source]

A view of the tunnel.
External links[edit  edit source]
 McNeil, Jim. "Simple Stewart toroids".
Bibliography[edit  edit source]
 Stewart, Bonnie (1964). Adventures Amoung the Toroids (2 ed.). ISBN 0686119 363.