Exploring Truncated Platonic Solids and Polyhedra Patterns
Discover what happens when vertices are symmetrically cut off from Platonic solid shapes, leading to changes in the numbers of faces, vertices, and edges. Explore relationships between the original Platonic values and the truncated values, and investigate similar patterns in other polyhedra shapes.
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truncated platonic solids what happens if you cut off all of the vertices symmetrically, a little bit of the way along each of the edges ? what happens to the numbers of faces vertices edges ?
cube Truncated tetrahedron Truncated cube tetrahedron F = 6 V = 8 E = 12 F = ? V = ? E = ? F = 4 V = 4 E = 6 F = ? V = ? E = ? For each 3D shape, can you find out the number of edges faces and vertices when we cut of the vertices? dodecahedron octahedron F = 12 V = 20 E = 30 F = 8 V = 6 E = 12 Truncated dodecahedron Truncated octahedron F = ? V = ? E = ? F = ? V = ? E = ?
icosahedron F = 20 V = 12 E = 30 truncated icosahedron (football) F = ? V = ? E = ?
Now fill in this table with all of your results platonic tetrahedron F, V, E 4, 4, 6 truncated F , V , E cube 6, 8, 12 octahedron dodecahedron 8, 6, 12 12, 20, 30 icosahedron 20, 12, 30 what relationships are there between the platonic values and the truncated values? Can you find the link between (a) E and F (b) E and V (c) E and E
trying other polyhedra (does the pattern still work?) F = 5 V = 6 E = 9 F = V = E = F = 5 V = 5 E = 8 F = V = E =
