In crystallography, the regular or ordinary dodecahedron is an impossible form since the faces cut the axes in irrational ratios; the "pentagonal dodecahedron" of crystallographers has irregular pentagons for faces, while the geometrical solid, on the other hand, has regular ones.
However, the American mathematician George Birkhoff showed in 1913 that a particular arrangement of four adjacent pentagons is reducible.
Three pentagons may be placed at a common vertex to form a solid angle, and by forming several such sets and placing them in juxtaposition .a solid is obtained having 12 pentagonal faces, 30 edges, and 20 vertices.
Square or rectangular wedding cakes look classic with their clean lines, and more unusual shapes, such as hexagons or pentagons, make for beautiful presentations.
Then move to pentagons (5 sides), hexagons (6 sides), and octagons (8 sides), etc. if it appears that children have mastered the first set of shapes.