Hessian polyhedron

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Hessian polyhedron
Rank3
TypeRegular
SpaceComplex
Notation
Coxeter diagram
Schläfli symbol
Elements
Faces27 Möbius–Kantor polygons
Edges72 3-edges
Vertices27
Vertex figureMöbius–Kantor polygon
Related polytopes
Real analog221 polytope
DualHessian polyhedron
Van Oss polygonγ 3
2
 
Abstract & topological properties
Flag count648
Properties
Symmetry3[3]3[3]3, order 648

The Hessian polyhedron is a regular complex polyhedron. It is self-dual.

Coxeter diagrams[edit | edit source]

Related polytopes[edit | edit source]

The relationship between the three Platonic solids (left), and the analygous relationship between the three Hessian polyhedra (right)

The three regular complex polyhedra:

  1. the Hessian polyhedron
  2. the double Hessian polyhedron
  3. the rectified Hessian polyhedron

share analogous relationships to three Platonic solids:

  1. the tetrahedron
  2. the cube
  3. the octahedron

Those relationships are:

  • 1 is self-dual.
  • 2 is dual to 3.
  • 1 is the halving of 2.
  • 3 is the rectification of 1.

If the vertices of the Hessian polyhedron are treated as vertices in rather than , they are identical to those of the 221 polytope.

External links[edit | edit source]