Double Hessian polyhedron

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Double Hessian polyhedron
Rank3
TypeRegular
SpaceComplex
Notation
Coxeter diagram
Schläfli symbol
Elements
Faces72
Edges216 dyads
Vertices54
Vertex figureMöbius–Kantor polygon
Related polytopes
DualRectified Hessian polyhedron
HalvingHessian polyhedron
Van Oss polygonHexagon
Abstract & topological properties
Flag count1296
Properties
Symmetry2[4]3[3]3, order 1296

The double Hessian polyhedron is a regular complex polyhedron. It's vertices are equivalent to a pair of dual Hessian polyhedra.

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 Double Hessian polyhedron are treated as vertices in rather than , they are identical to those of the Bidodecateric heptacontadipeton.

External links[edit | edit source]