Dodecahedron in Geometry
In geometry, a dodecahedron is any polyhedron with twelve flat faces, usually pentagonal. A regular dodecahedron is a Platonic solid. It is one of the five Platonic solids, and the one with the most sides. There are also three regular star dodecahedra. A small stellated dodecahedron has as its faces 12 pointy stars, seen as extending from the center of the dodecahedron outwards. If the central pentagon is equilateral, and each edge of that pentagon is parallel to a corresponding edge on another pentagon, then we have a regular compound of two dodecahedra.
Dodecahedral Symmetry
A dodecahedron has twelve faces, twenty vertices, and thirty edges. The symmetry group of a dodecahedron is the dihedral group D5h of order 120 (isomorphic to (Z/2Z)5 × S5), order 2+10×5!/2 = 60 dihedral symmetries.
Dual polyhedron: Icosahedron
Symmetry group: Dihedral group D5h of order 120 [3] (isomorphic to (Z/2Z)5 × S5), order 2+10×5!/2 = 60 dihedral symmetries
FAQ
What is a dodecahedron in geometry?
In geometry, a dodecahedron is any polyhedron with twelve flat faces, usually pentagonal. A regular dodecahedron is a Platonic solid. It is one of the five Platonic solids, and the one with the most sides. There are also three regular star dodecahedra. A small stellated dodecahedron has as its faces 12 pointy stars, seen as extending from the center of the dodecahedron outwards. If the central pentagon is equilateral, and each edge of that pentagon is parallel to a corresponding edge on another pentagon, then we have a regular compound of two dodecahedra.
Why is it called a dodecahedron?
The word dodecahedron comes from the Greek words for "twelve" and "faces."
What are the properties of a dodecahedron?
A dodecahedron has twelve faces, twenty vertices, and thirty edges. The symmetry group of a dodecahedron is the dihedral group D5h of order 120 (isomorphic to (Z/2Z)5 × S5), order 2+10×5!/2 = 60 dihedral symmetries.
What type of polygon is a dodecahedron?
A dodecahedron is a polyhedron with twelve flat faces, usually pentagonal. There are also three regular star dodecahedra. A small stellated dodecahedron has as its faces 12 pointy stars, seen as extending from the center of the dodecahedron outwards. If the central pentagon is equilateral, and each edge of that pentagon is parallel to a corresponding edge on another pentagon, then we have a regular compound of two dodecahedra.
