Cake pan

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Cake pan
Rank3
TypeQuasi-convex Stewart toroid
Notation
Stewart notationQ3P6/P3Q3
Elements
Faces3+3+3+3+3 squares, 3+3 triangles
Edges3+3+3+3+3+3+3+6+6+6
Vertices3+3+6+6
Measures (edge length 1)
Volume
Surface area
Related polytopes
Convex hullElongated triangular cupola
Abstract & topological properties
Flag count156
Euler characteristic0
SurfaceTorus
OrientableYes
Genus1
Properties
SymmetryA2×I, order 6
Flag orbits26
ConvexNo

The cake pan is a quasi-convex 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]

External links[edit | edit source]

Bibliography[edit | edit source]

  • Stewart, Bonnie (1964). Adventures Amoung the Toroids (2 ed.). ISBN 0686-119 36-3.