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.