Regular polyhedrons are those whose faces are all regular polygons, congruent to each other, whose polyhedral angles are all equal and which has the same number of faces meet at each vertex. For a regular polygon of n-sides, this polygonal pyramid will become a circular cone in the limit. We may also think of a polygonal pyramid with the base as a polygon of n-sides. A fourth non-parallel plan is needed to get a polyhedron of least order – 4 faces, 6 edges and 4 vertices this is known as a Tetrahedron or sometimes as triangular pyramid. But three intersecting planes still do not make a closed polyhedron. The solid angle at the vertex of a typical polyhedron is known as a polyhedral angle, made by three or more planes.

This solid angle is referred to as trihedral angle, as they are made by three planes. Three planes which are non parallel to each other make a solid angle at a unique point of intersection of all the three planes.

Similarly, two non-parallel planes make an angle all along the common edge. Two non-parallel straight lines in a plane make an angle. Three straight lines in a plane which are non parallel to each other make a triangle, which is a polygon of least order – 3 sides and 3 angles. In the limit the regular polygon becomes a circle.Įxtending to the third dimension, there are infinite numbers of polyhedrons, starting from tetrahedron. Polygons with all sides and all internal angles equal are called regular polygons and there are infinite numbers of regular polygons with 3 to infinite numbers of sides. Starting from triangle, quadrilateral and pentagon, there are infinite number of polygons. As I learnt more of plane geometry, I developed a habit of extending the results of the theorems to the third dimension. But he was rather surprised that I understood a lot of what he told me especially in geometry. When I was around as a young boy, he would do the explaining to me, not caring how much of it I understood.

He had a habit of reading and explaining to himself as a part of his study process. I was introduced to Solid Geometry by my elder brother (L V Sundaram) when I was barely 10 years old. Solid geometry has always fascinated me and has fired up my imaginative power.

Octahedron angles between faces