Paperweight puzzle

This page concerns a less successful definition of "regular", intended for polyhedra, though it could be applied to regular maps with similar results.

The definition is from a book of puzzlesSTA, most of them much better-defined than the one quoted. It is puzzle no. 28, appearing on page 22. Here it is:


Dr. Whatknot, when I saw him the other day, was very pleased with his new paperweight. This is a perfectly symmetrical solid figure; that is to say, before it was painted, on whichever of its faces it stood, it presented exactly the same appearance.

Three of its faces are now painted red, three are painted blue. The other six are uncoloured.

What is the shape of each face?

How many answers are possible? Let us assume that a paperweight must have plane, simply connected, faces. Then the puzzle can be specified as:

A polyhedron is convex, face-transitive, and has 12 faces. What shape could its faces be?

Try to answer this yourself before checking my answers.

This page relates to What do we mean by "Regular" for Orientable Regular Maps?
Index to other pages on regular maps.

Copyright N.S.Wedd 2012