Quick Math Homework Help
Master the 7 pillars of school success
Improve your grades and lower your stress
Platonic Solids
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.
Cube
- 3 squares at each corner.
- 6 square faces.
- 8 vertices
- 12 edges
Tetrahedron
- 3 equilateral triangles at each corner.
- 4 triangle faces.
- 4 vertices
- 6 edges
Octahedron
- 4 equilateral triangles at each corner
- 8 triangle faces
- 6 vertices
- 12 edges
Icosahedron
- 5 equilateral triangles at each corner
- 20 triangle faces
- 12 vertices
- 30 edges
Dodecahedron
- 3 pentagons at each corner
- 12 pentagon faces
- 20 vertices
- 30 edges
Interesting Facts about Platonic Solids
5 Platonic Solids
Platonic Solids
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.