Regular polygons
(with side length, s)
A uniform polyhedron has regular polygons as faces, such that for every two vertices there is an isometry mapping one into the other (just as there is for a regular polygon).
A quasiregular polyhedron is a uniform polyhedron which has just two kinds of face alternating around each vertex.
A regular polyhedron is a uniform polyhedron which has just one kind of face.
The remaining (non-uniform) convex polyhedra with regular faces are known as the Johnson solids.
A polyhedron having regular triangles as faces is called a deltahedron.
See also
- Euclidean tilings by convex regular polygons
- Platonic solid
- Apeirogon – An infinite-sided polygon can also be regular, {∞}.
- List of regular polytopes and compounds
- In addition, the regular star figures (compounds), being composed of regular polygons, are also self-dual.
A uniform polyhedron has regular polygons as faces, such that for every two vertices there is an isometry mapping one into the other (just as there is for a regular polygon).
A quasiregular polyhedron is a uniform polyhedron which has just two kinds of face alternating around each vertex.
A regular polyhedron is a uniform polyhedron which has just one kind of face.
The remaining (non-uniform) quasiregular polyhedron is a uniform polyhedron which has just two kinds of face alternating around each vertex.
A regular polyhedron is a uniform polyhedron which has just one kind of face.
The remaining (non-uniform) convex polyhedra with regular faces are known as the Johnson solids.
A polyhedron having regular triangles as faces is called a deltahedron.
f := proc (n) options operator, arrow; [ [convert(1/4*n*cot(Pi/n), radical), convert(1/4*n*cot(Pi/n), float)], [convert(1/2*n*sin(2*Pi/n), radical), convert(1/2*n*sin(2*Pi/n), float), convert(1/2*n*sin(2*Pi/n)/Pi, float)], [convert(n*tan(Pi/n), radical), convert(n*tan(Pi/n), float), convert(n*tan(Pi/n)/Pi, float)] ] end proc
The expressions for n=16 are obtained by twice applying the tangent half-angle formula to tan(π/4)
