Rectified Hessian polyhedron

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Rectified Hessian polyhedron
Rank3
TypeRegular
SpaceComplex
Notation
Coxeter diagram
Schläfli symbol
Elements
Faces54 Möbius–Kantor polygons
Edges216 3-edges
Vertices72
Vertex figure
Related polytopes
DualDouble Hessian polyhedron
Abstract & topological properties
Flag count1296
Properties
Symmetry3[3]3[4]2, order 1296

The rectified Hessian polyhedron is a regular complex polyhedron.

Coxeter diagrams[edit | edit source]

A rectified Hessian polyhedron can be represented by the following Coxeter diagrams:

  • (full symmetry)
  • (L3 symmetry)

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:

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

External links[edit | edit source]