Quick Math Homework Help

A platonic solid is a convex **Polyhedron** that satisfy these three characteristics:

- Made up of regular polygons.

- All faces are congruent.

- All corners are congruent.

- The same number of faces meet at every vertex.

3 Platonic solids are made of equilateral triangles

tetrahedron, octahedron, icosahedron

One platonic solid is made of squares, a cube.

One platonic solid is made of pentagons, a dodecahedron.

Here are the 5 platonic solids and their characteristics.

- 3 squares at each corner.

- 6 square faces.

- 8 vertices

- 12 edges

- 3 equilateral triangles at each corner.

- 4 triangle faces.

- 4 vertices

- 6 edges

- 4 equilateral triangles at each corner

- 8 triangle faces

- 6 vertices

- 12 edges

- 5 equilateral triangles at each corner

- 20 triangle faces

- 12 vertices

- 30 edges

- 3 pentagons at each corner

- 12 pentagon faces

- 20 vertices

- 30 edges

The ancient Greeks were fascinated by the Platonic solids and studied them intensely.

Plato associated our planet with the platonic solids and described the Earth with the cube, air with the octahedron, the icosahedron was water, and the tetrahedron was linked with fire.

The angles at all vertices of all faces of a Platonic solid are identical

Each vertex of each face of a platonic solid must contribute less than 120°.

The tetrahedron, octahedron, and icosahedron all have triangular faces.

The cube is the only platonic solid with a square face..

The dodecahedron is the only platonic solid with a face in the shape of a pentagon.

The tetrahedron, cube, and octahedron are seen in crystal structures.

Some virus has the shape of a regular icosahedron.

The internal angles that meet at a vertex of a platonic solid must,be less than 360 degrees or the shape lies flat.

If you had six triangles the angle measure would equal 6 x 60 = 360, therefore the shape would be flat.

There are at least 3 faces at each vertex of platonic solids.