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 type of solid is a dodecahedron?
A dodecahedron is a platonic solid that consists of 12 sides and 12 pentagonal faces. The properties of a dodecahedron are: A dodecahedron has 12 pentagonal sides, 30 edges, and 20 vertices and at each vertex 3 edges meet. The platonic solid has 160 diagonals.
Is dodecahedron 3D or 2D?
3D shape
A Dodecahedron is a 3D shape with twelve faces. Each of those faces is a regular pentagon. A pentagon is a 2D shape with five sides.
What is a dodecahedron used for?
Speculative uses include as survey instruments for estimating distances to (or sizes of) distant objects, or devices for determining the optimal sowing date for winter grain.
What are the properties of a dodecahedron?
A regular dodecahedron or pentagonal dodecahedron is a dodecahedron that is regular, which is composed of 12 regular pentagonal faces, three meeting at each vertex. It is one of the five Platonic solids. It has 12 faces, 20 vertices, 30 edges, and 160 diagonals (60 face diagonals, 100 space diagonals).
Is a dodecahedron a Platonic solid?
Platonic solid, any of the five geometric solids whose faces are all identical, regular polygons meeting at the same three-dimensional angles. Also known as the five regular polyhedra, they consist of the tetrahedron (or pyramid), cube, octahedron, dodecahedron, and icosahedron.
What is a 3d shape with 12 sides called?
By: Mark Mancini | Jul 21, 2020. Dodecahedrons are three-dimensional bodies containing a dozen flat faces — all shaped like pentagons. HowStuffWorks.
What is special about 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.
Who invented the dodecahedron?
When Hippasus of Metapontum (who is credited with discovering the dodecahedron) divulged the secret of the existence of the irrational, he was thrown in the river and drowned. Phi, expressed to about 20,000 places is printed to the surface in the painting. Pythagoras discovered the mathematics in music.
How many sides are there in a dodecahedron?
12
A regular dodecahedron or pentagonal dodecahedron is a dodecahedron that is regular, which is composed of 12 regular pentagonal faces, three meeting at each vertex. It is one of the five Platonic solids….
| Regular dodecahedron | |
|---|---|
| Faces by sides | 12{5} |
| Conway notation | D |
| Schläfli symbols | {5,3} |
| Face configuration | V3.3.3.3.3 |
What do you call a 3d shape with 20 sides?
In geometry, an icosahedron (/ˌaɪkɒsəˈhiːdrən, -kə-, -koʊ-/ or /aɪˌkɒsəˈhiːdrən/) is a polyhedron with 20 faces.
What is the shape of a dodecahedron?
“In geometry, a dodecahedron is any polyhedron with twelve flat faces, but usually a regular dodecahedron is meant: a Platonic solid. It is composed of 12 regular pentagonal faces, with three meeting at each vertex, and is represented by the Schläfli symbol {5,3}.
What is the difference between Platonic solids and dodecahedrons?
Platonic solids are convex polyhedra in which the faces are made up of congruent regular polygons with the same number of faces meeting at each of their vertices. A dodecahedron is made up of 12 congruent pentagons with 3 pentagonal faces meeting at each of its 20 vertices. There are two types of dodecahedrons – regular and irregular dodecahedrons.
How many pentagons are in a dodecahedron?
Like the regular dodecahedron, it has twelve identical pentagonal faces, with three meeting in each of the 20 vertices (see figure). However, the pentagons are not constrained to be regular, and the underlying atomic arrangement has no true fivefold symmetry axis.
What is the combinatorial structure of dodecahedra?
Some dodecahedra have the same combinatorial structure as the regular dodecahedron (in terms of the graph formed by its vertices and edges), but their pentagonal faces are not regular: The pyritohedron, a common crystal form in pyrite, has pyritohedral symmetry, while the tetartoid has tetrahedral symmetry .