Objective:
Students will be able to explain how polyhedra are named by understanding the relationships between polyhedra.Materials:
Answer: tetrahedron ( 4 faces)cube or hexahedron ( 6 faces)
octahedron ( 8 faces)
dodecahedron (12 faces)
icosahedron (20 faces)
Answer: Truncation means "cutting off the vertices". You show the truncation of a Platonic solid on KaleidoTile by dragging the Basepoint along the edge in the Basepoint window.
Answer: The cuboctahedron is obtained by complete truncation of either the cube or the octahedron. Likewise for the icosadodecahedron.
Answer: The true answer to this is a bit complex. Students should make a connection between the red (medium shaded) squares that arise in the polyhedra with rhombi in the naming. You could make the connection that the etymology of rhombi meant a square.
Answer: Both namings are correct. The octahedron does not really belong to the (2,3,3)-family, however it is formed by the complete truncation of the tetrahedron. By naming this octahedron a tetratetrahedron, you are understanding that the color (or shading) matters. KaleidoTile's naming system doesn't take that into consideration.
Answer: You should get answers that tie the different parts of the name together. Dodeca (12 sides) and icosa (20 sides) combine to produce an icosadodecahedron. This is then truncated (vertices cut off) producing a square (rhombi) face where each vertex was.
It is recommended that you show the video The Platonic Solids by Key Curriculum Press. The video describes the Platonic solids, explains why there are only five of them, and discusses duals of polyhedra.