An icosahedron has the maximum number of faces (i.e., 20).
Tetrahedron, cube, octahedron, icosahedron, and dodecahedron are the only 5 platonic solids.
Shapes - Dodecahedron shapes can be seen in many real-life situations like the Roman dodecahedron, dodecahedron dice, etc.
Angles - The angle between sides of the pentagon: 108° and the angle of intersection of 2 adjacent faces (Dihedral angle) : 116.56505°.
The sum of the angles at each vertex is, 3 x 108° = 324°.
Vertices - It has 20 Vertices (corner points), and at each vertex 3 edges meet.
Sides - A dodecahedron has 12 pentagonal sides.
Let us learn some important properties (sides, edges, shapes, vertices, angles) related to the dodecahedron. The dodecahedron has 31 such different paths. Is it possible to go in a straight line and return to your house without going through your neighbors' houses? You'd most likely assume that the answer is - no!įor over 2000 years, mathematicians have known about platonic solids but recently, a group of 3 mathematicians - Jayadev Athreya, David Aulicino, and Patrick Hooper found the solution to this problem in a dodecahedron. Every morning you go on a jog, you run in a straight line, never turn or change your path. Your neighbors are living in the other vertices. Let's assume that you are living in one of the platonic solids, and you have a house in one of the vertices. The dodecahedron definition can be better understood using this illustration. Hence, any polyhedra with 12 sides can be called a dodecahedron. Dodecahedron is derived from the Greek word "dōdeka" means "12" and "hédra" means "face or seat" that shows that it is a polyhedron with 12 sides or 12 faces.
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