The 5 regular polyhedra are called a tetrahedron, hexahedron, octahedron, dodecahedron and icosahedron with 4, 6, 8, 12, and 20 sides respectively.

Non-polyhedrons are cones, spheres, and cylinders because they have sides that are not polygons. A prism is a polyhedron with two congruent bases, in parallel planes, and the lateral sides are rectangles.

Cylinders, cones, and spheres are not polyhedrons, because they have curved, not flat, surfaces. A cylinder has two parallel, congruent bases that are circles. A cone has one circular base and a vertex that is not on the base.

A polyhedron is a 3D-shape that has flat faces, straight edges, and sharp vertices (corners). The word “polyhedron” is derived from a Greek word, where ‘poly’ means “many” and hedron means “surface”. Thus, when many flat surfaces are joined together they form a polyhedron….What is a Polyhedron.

A polyhedron is a three-dimensional figure composed of faces. Each face is a filled-in polygon and meets only one other face along a complete edge. The ends of the edges meet at points that are called vertices. A polyhedron always encloses a three-dimensional region. The plural of polyhedron is polyhedra.

The most familiar example of a polyhedron is a cube. Its faces are squares, and it has 6 of them. It also has 12 edges and 8 vertices. Another familiar example is a pyramid.

If all of the sides are the same shape and size, the figure is called a regular polyhedron. The regular polyhedra that we will be seeing are a triangular pyramid whose sides are all equilateral triangles, and a cube (a square prism) whose sides are all squares.

A particularly popular polyhedron is the pyramid. If we restrict ourselves to regular polygons for faces, there are three possible pyramids: the triangle-based tetrahedron, the square pyramid, and the pentagonal pyramid. Being bounded by regular polygons, these last two fall within the class of Johnson solids.

A hexahedron is a polyhedron with six faces. The unique regular hexahedron is the cube. Two hexahedra can be built from regular polygons with equal edge lengths: the equilateral triangular dipyramid and pentagonal pyramid.

A rectangular pyramid consists of five faces; one rectangular-shaped base and four triangular-shaped faces. Each triangular face is congruent to the opposite face.

An equilateral triangular based prism has four planes of symmetry. A rectangular based pyramid has 2 planes of symmetry. A square based pyramid has 4 planes of symmetry.

A 3 sided pyramid with planar sides is impossible. One with a square base has 5 sides and one with a triangular base has 4. To have 3 sides it would have a line as a base!