Another Irregular Dodecahedron

The pentagons on this irregular pentagonal dodecahedron are not convex; one vertex is "pushed in."

Question: The outer vertices of this dodecahedron are the vertices of what polyhedron?

Question: The inner vertices of this dodecahedron are the vertices of what polyhedron?

Nonconvex models are always tricky to build. First, glue the tabs with matching circles. This pattern can be repeated to complete the model. It is easiest to leave a convex vertex for the last one; that is, be sure that your last pair of tabs completes a vertex where three of the shorter edges meet.

WARNING! This small model should be attempted by experienced model builders only. See below for a larger model.

You will need three copies of this net. When creasing, fold the long-dashed lines "up".

Build this by looking at the picture and using the rule that the ends of long-dashed lines should never touch.

• How to build a model.
• Another example of an irregular pentagonal dodecahedron.