What is special about a dodecahedron?
While the regular dodecahedron shares many features with other Platonic solids, one unique property of it is that one can start at a corner of the surface and draw an infinite number of straight lines across the figure that return to the original point without crossing over any other corner.
What are the angles in a dodecahedron?
Table of polyhedron dihedral angles
| Name | Schläfli symbol | dihedral angle – exact in bold, else approximate (degrees) |
|---|---|---|
| Platonic solids (regular convex) | ||
| Hexahedron or Cube | {4,3} | 90° |
| Octahedron | {3,4} | 109.471° |
| Dodecahedron | {5,3} | 116.565° |
What is a dodecahedron in geometry?
The regular dodecahedron, often simply called “the” dodecahedron, is the Platonic solid composed of 20 polyhedron vertices, 30 polyhedron edges, and 12 pentagonal faces, . It is also uniform polyhedron and Wenninger model . It is given by the Schläfli symbol and the Wythoff symbol .
What does the dodecahedron symbolize?
A dodecahedron is any polyhedron with twelve faces. Three faces meet at each vertex. It is dual to the regular icosahedron. The dodecahedron is said to represent the universe; while the other four Platonic solids represent earth, fire, water and air, the five elements.
Who invented the dodecahedron?
Abstract: The dodecahedron is a beautiful shape made of 12 regular pentagons. It doesn’t occur in nature; it was invented by the Pythagoreans, and we first read of it in a text written by Plato.
What is represented by the Platonic solid dodecahedron?
The 5 platonic solids are considered cosmic solids due to their connection to nature that was discovered by Plato. The cube represents the earth, the octahedron represents the air, the tetrahedron represents the fire, the icosahedron represents the water, and the dodecahedron represents the universe.
What are the properties of a dodecahedron?
Properties of Dodecahedrons 1 Sides – A dodecahedron has 12 pentagonal sides. 2 Edges – A dodecahedron has 30 edges. 3 Vertices – It has 20 Vertices (corner points), and at each vertex 3 edges meet. 4 It has 160 diagonals. 5 The sum of the angles at each vertex is, 3 x 108° = 324°.
Is the rhombic dodecahedron a semi regular polyhedron?
The rhombic dodecahedron (hereinafter, referred to as r.d.) is a semi-regular polyhedron, in that all of its edges are the same length, yet the angles of its faces differ.
What are the properties of a parallelogram in geometry?
Consecutive angles are supplementary (A + D = 180°). If one angle is right, then all angles are right. The diagonals of a parallelogram bisect each other. Each diagonal of a parallelogram separates it into two congruent triangles. If we have a parallelogram where all sides are congruent then we have what is called a rhombus.
What is the sum of all the angles of a dodecahedron?
We know, the interior angle of the dodecahedron is 108°. A dodecahedron has a pentagonal face. Hence, the sum of all the angles of one face of a dodecahedron is 108° × 5 = 540° A dodecahedron has 12 pentagonal faces. Thus, the sum of all the angles of the dodecahedron is 540 × 12 = 6480.