Oriental hat

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Oriental hat
Rank3
TypeQuasi-convex Stewart toroid
Notation
Stewart notationR5/S5Q5
Elements
Faces5 pentagons, 5 squares, 5+5+5+5+5 triangles
Edges60
Vertices10+5+5+5
Measures (edge length 1)
Central density0
Related polytopes
Convex hullPentagonal rotunda
Abstract & topological properties
Flag count240
Euler characteristic0
OrientableYes
Genus1
Properties
SymmetryH2×I, order 10
Flag orbits24
ConvexNo

The oriental hat is a quasi-convex Stewart toroid. It can be made by excavating a pentagonal rotunda by a pentagonal antiprism and a pentagonal cupola.

Vertex coordinates[edit | edit source]

The vertex coordinates for a tunnelled pentagonal rotunda with edge length 1 can be given as:

  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • .

Related polytopes[edit | edit source]

The two elongations of the oriental hat differ in the shape of their tunnels.

The oriental hat can be elongated in two ways to form quasi-convex Stewart toroids, both with the elongated pentagonal rotunda as their convex hull.[1] It cannot be gyroelongated.

12 tunnelled pentagonal rotundae are used in the construction of the Webb toroid.

Gallery[edit | edit source]

External links[edit | edit source]

References[edit | edit source]

  1. Stewart (1964:37)

Bibliography[edit | edit source]

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