Answer to Question #135556 in Geometry for Thembeka

Question

Name and define the five Platonic solids and their characteristics.

Answer 1

A Platonic solid is a regular, convex polyhedron in a three-dimensional space with equivalent faces composed of congruent convex regular polygonal faces. The five solids that meet this criterion are the tetrahedron, cube, octahedron, dodecahedron, and icosahedron.

Properties Of Platonic Solids

To be a Platonic solid, the tested shape must:

Be convex

Be three-dimensional (a polyhedron)

Have congruent faces

Have congruent corners (vertices)

Here are the five Platonic Solids and their relationships to two-dimensional shapes:

Tetrahedron has four triangular faces

Tetrahedron has four vertices with three triangular faces meeting

Cube has six square faces

Cube has eight vertices with three square faces meeting

Octahedron has eight triangular faces

Octahedron has six vertices with four triangular faces meeting

Dodecahedron has 12 pentagonal faces

Dodecahedron has 20 vertices with three pentagonal faces meeting

Icosahedron has 20 triangular faces

Icosahedron has 12 vertices with five triangular faces meeting