Schlegel Diagrams

vertices

4

5

6

7

8

9

10

pick polyhedron (34)

1

outer face

1

2

3

4

5

6

poly graph - V: 7 F: 6 E: 11

g6 form:

Fxo[g

faces

{2,3,4,6,5}

{5,6,7,1}

{6,4,7}

{3,2,1}

{1,2,5}

{1,7,4,3}

A Schlegel diagram is a planar 2D representation of a polyhedron with the following properties:

1. One outer face is taken as a regular polygon.

2. The inner faces are convex polygons.

3. Sometimes, faces are colored according to the number of edges.

There is just one tetrahedron. After that, there are two pentahedra, seven hexahedra, 34 heptahedra, 257 octahedra, 2606 nonahedra, and 32300 decahedra. This Demonstration draws Schlegel diagrams for all of these polyhedra.

References

[1] Wikipedia. "Schlegel Diagram." (Jun 6, 2016) en.wikipedia.org/wiki/Schlegel_diagram.

External Links

Schlegel Graph (Wolfram MathWorld)

Permanent Citation

Ed Pegg Jr

"Schlegel Diagrams"
http://demonstrations.wolfram.com/SchlegelDiagrams/
Wolfram Demonstrations Project
Published: June 7, 2016