Polyhedra

Solids bounded by flat faces. They are drawn by their edges: visible with a continuous line, hidden with a dashed one.

Cube resting on the horizontal plane

STEP 1 / 3

The base

Resting on the PH, the base is a square seen in true size in the plan. In the elevation, the base projects onto the ground line.

Intersection of a line with a solid

STEP 1 / 3

Line crossing the solid

Line r enters and leaves the prism at two points. Those two penetration points are what we are looking for.

The five regular solids: tetrahedron (4 triangles), cube (6 squares), octahedron (8 triangles), dodecahedron (12 pentagons) and icosahedron (20 triangles).

The five regular solids, in numbers

Worth memorising faces, edges and vertices (they satisfy V - E + F = 2):

Tetrahedron: 4 triangular faces, 6 edges, 4 vertices. Height = a·√(2/3) ≈ 0.8165·a.
Cube: 6 square faces, 12 edges, 8 vertices. Diagonal = a·√3.
Octahedron: 8 triangular faces, 12 edges, 6 vertices.
Dodecahedron: 12 pentagonal faces, 30 edges, 20 vertices.
Icosahedron: 20 triangular faces, 30 edges, 12 vertices.

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