Polyhedra examples

Links from this page allow you to download a dodecal calendar for 2025 in Draw format

(size 26K)
or in PDF format (size 11K)
and to see examples of the kinds of things you can do with:

!PolyDraw
!PolyNet
!Stellate

!PolyDraw

has data to draw over 140 different polyhedra, these are accessed via a 'PolyList' file which can be changed by the user who wants to add their own polyhedra, for example the exciting new ones which you have made using !Stellate. A 'Selections' window is used to reduce the number of polyhedra to choose from, for example you might want to look only at 'Archimedean Duals', only those made from triangles, or only those which have more than 50 faces. Click here to see an example of the screen.
Click here to download a demo version of the program (size 397K).
Click here to see examples of some polyhedra, mostly compounds and stellations.

!PolyNet

allows you to make your own planar nets interactively, or to add tabs to any of the nets provided as !PolyDraw data. You simply drag a data file to !PolyNet on the iconbar which opens the 3D working window, you click on any face and another 'net' window opens, keep clicking on faces connected to one already in the net and you can make many different nets.

If you want to use the nets to print to card, cut it out and create a real 3D model then you can add gluing tabs and you own ideas of clip-art to the faces. You can make pretty boxes for a friend's birthday present or boxes for special occasions such as Christmas or Easter.

Click here to see a 3D shaded model of the compound of 2 tetrahedra surrounded by various examples of planar nets made using !Polynet.
Click here to download a demo version of the program (size 130K).

!Stellate

The process of stellation is explained here for the example of a regular Dodecahedron.

!Stellate is supplied with data to make more than 120 polyhedra, including all the 'Uniform Polyhedra' with their Duals and is able to make all their Stellations. Use these as starting points to create your own entirely new polyhedra. The package has extensive documentation, including a glossary of terms and a set of suggested activities to help you learn about stellations and their properties, a few explanations and diagrams can be seen here.
Click here to download a demo version of the program (size 604K).

A 'Uniform Polyhedron' has faces made of regular polygons with the same types of polygons arranged in the same order around all vertices. In his book 'Polyhedron Models' (Tarquin Press) Wenninger has arranged these in increasing complexity:

The Platonic solids (numbers 1-5) are convex and have only one type of polygon face;
The Archimedean solids (numbers 6-18) are convex and have two or three different types of faces;
Wenninger now includes some 'Stellations' (numbers 19-66) which are produced by extrapolating the faces of some of the Platonic and Archimedean solids;
Numbers 67 to 119 are the remaining 'Uniform Polyhedra' which are non-convex.

Click here to see polyhedra from 1 to 63 (83Kb)

Click here to see polyhedra from 64 to 119 and a few extra ones we particularly like (103Kb)

Click here to see the duals (74K) of the non-convex uniform solids made by !Stellate.
( The dual of a uniform solid is the one where there are faces in the directions of the original's vertices and vertices in the directions of the original's faces.)

Page last updated 4 November 2024
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