The Parametrized Szilassi Polyhedron

The following steps construct a seven-faced regular toroid, the Szilassi polyhedron.
1. Take a tetrahedron with isosceles triangles as faces.
2. Drill the tetrahedron with a three-sided prism, one of whose faces is parallel to the base of the isosceles triangles; the prism's opposing faces intersect two opposing edges of the tetrahedron. This gives a seven-faced polyhedron that has five hexagonal faces and two quadrilateral faces. (The top face and the bottom edges of the prism can be selected arbitrarily.)
3. Supplement the polyhedron with two small tetrahedra, the faces of which are aligned in the planes of the existing faces. Move the lower edge of the prism bisecting the edges of the triangle closer to the opposite face, so that the two quadrilaterals in (2) are extended to hexagons, parallel to the plane of the exterior face of the added tetrahedra.
4. This gives a seven-faced polyhedron. Any two faces of this polyhedron are adjacent, and a vertex of two faces are on an opposite edge.
In 1977, a different procedure led to the discovery of this polyhedron.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+