# Message #3275

From: Melinda Green <melinda@superliminal.com>

Subject: Re: [MC4D] Császár and Szilassi polyhedra

Date: Mon, 14 Dec 2015 14:53:52 -0800

Interesting! Is it at all related to the holyhedron

<https://en.wikipedia.org/wiki/Holyhedron>or the flexible Steffen model

<http://mathworld.wolfram.com/FlexiblePolyhedron.html>? It looks a lot

like the Steffen model which also happens to contains 14 triangular faces.

-Melinda

On 12/12/2015 3:14 PM, Roice Nelson roice3@gmail.com [4D_Cubing] wrote:

>

>

> Yesterday I learned about the Császár polyhedron

> <http://www.futilitycloset.com/2015/12/10/the-csaszar-polyhedron> on

> Google+.

>

> plus.google.com/u/0/+DavidJoyner/posts/HEBGDgqLgdG

> <http://plus.google.com/u/0/+DavidJoyner/posts/HEBGDgqLgdG>

>

> It is the only known polyhedron besides the tetrahedron that has no

> diagonals - all 7 vertices connect to every other. With 21 edges and

> 14 faces, its genus is 1. You can think of it as the complete graph

> <https://en.wikipedia.org/wiki/Complete_graph> K_7 embedded on the

> torus. It also has a dual, the Szilassi polyhedron

> <https://en.wikipedia.org/wiki/Szilassi_polyhedron>. Both relate to

> the Heawood graph

> <http://blogs.ams.org/visualinsight/2015/08/01/heawood-graph/>.

>

> Turns out I already had the latter configured in MagicTile (the {6,3}

> 7-Color), but I didn’t have the former, so I just added it. Here are

> some pictures of the tilings.

>

> https://goo.gl/photos/K1vYapeTqqYteGx58

> https://goo.gl/photos/kQMxQCtbCqsL2Wj88

>

> Both are in the Euclidean/Torus section of MagicTile.

>

> www.gravitation3d.com/magictile <http://www.gravitation3d.com/magictile>

>

> Enjoy!

> Roice

>

>

>

>

>