A polyhedron is a geometrical 3D shape whose faces are all polygons. A regular polygon is a 2D shape that has equal length sides as well as equal interior angles. A regular polyhedron, therefore, is a polyhedron with sides that are all equal regular polygons that meet at their vertices. Each vertex on a regular polyhedron connects an equal number of regular polygons. These figures have been studied since ancient times by the Greeks, and remnants of architecture has been uncovered in Scotland as well as Egypt.
There are five currently known regular polyhedra. Three have been formed with regular triangles: the tetrahedron with 4 faces, the octahedron with 8 faces, and the icosahedron with 20 faces. The commonly used cube is also a polyhedron with equilateral squares for faces, and the dodecahedron is represented as a 12-sided shape with pentagonal faces. The five known regular polyhedra can be seen here.
The Greeks believed these to be the only regular polyhedra possible. In this lab, we will attempt to prove (or disprove) this theory of the ancient Greeks. We also plan to analyze the truncation of these regular polyhedra. Truncating is when the vertices of a 3D shape are cut off, creating a shape in their place. Truncating a regular polyhedron at all vertices can create entirely new shapes and this interesting phenomenon will be explored further. As we delve further into the lab, more questions might arise that we will analyze and perhaps attempt to answer.