3-D

The Stellated Truncated Icosahedron, made of Sonobe Units

Matthew King

The Stellated Truncated Icosahedron, made of Sonobe Units  by Matthew King

This entry shows the strength of mathematical polyhedral, as this model is made entirely without glue or anything but ordinary paper. It is still quite stable because the various parts depend on each other for stability. It also shows an application of the famous "Four Color Theorem," which states that any planar graph can be colored with only four colors. Although this is not a planar graph, careful observation shows that this polyhedra never has two pieces of paper of the same color meet at the same peak. The mathematical significance of this model is that it shows that hexagons tile the plane and pentagons do not. In other words, regular hexagons can be drawn to fill an entire sheet of paper, but pentagons cannot.

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