Question

A polyhedron must meet three conditions in order to be regular:

All of the faces are regular polygons;

All of the faces are congruent (identical);

All of the vertex points/arrangements are congruent (identical).

Try to find three nonregular polyhedra, each of which violates a different one of these conditions. In other words, one of them should meet (1) and (2) but not (3); one should meet (1) and (3), but not (2); one should meet (2) and (3) but not (1). Describe each polyhedron using words:

number of faces and the polygons forming the faces

number of vertices and their vertex arrangements

number of edges

** Make sure to state which condition is being violated in each case

Answer 1