How many sides are in a dodecahedron?
Shown in the above figure are the three-dimensional objects and their flattened one-, two-dimensional images. From left to right the solids are tetrahedron (four sides), cube (six sides), octahedron (eight faces), dodecahedron (twelve faces), and icosahedron (twenty faces).
How many flat sides does a dodecahedron have?
twelve flat faces
In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka “twelve” + ἕδρα hédra “base”, “seat” or “face”) or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid.
Is dodecahedron a 2D 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. Like all 3D shapes, it’s possible to assemble a dodecahedron using a net.
How many symmetries does a dodecahedron have?
Symmetry groups of Platonic solids
|Number of faces||Number of edges|
How many vertices and faces does the dodecahedron have?
The Dodecahedron The dodecahedron has 30 edges, 20 vertices and 12 faces. Dodeca is a prefix meaning “twelve.” The dodecahedron is the only polyhedron I know of which is composed entirely of pentagons.
What is the ratio of a regular dodecahedron to a cube?
The ratio of the edge of a regular dodecahedron to the edge of a cube embedded inside such a regular dodecahedron is 1 : ϕ, or ( ϕ − 1) : 1. 2 : 1, or (5 + √5 ) : 4. For example, an embedded cube with a volume of 64 (and edge length of 4), will nest within a regular dodecahedron of volume 64 + 32 ϕ (and edge length of 4 ϕ − 4).
What is the dihedral angle of a regular dodecahedron?
The dihedral angle of a regular dodecahedron is 2 arctan (ϕ) or approximately 116.565 ° (where again ϕ = 1 + √ 5 2, the golden ratio). OEIS : A137218 Note that the tangent of the dihedral angle is exactly −2. If the original regular dodecahedron has edge length 1, its dual icosahedron has edge length ϕ.
How to calculate the area of a dodecahedron?
Enter one value and choose the number of decimal places. Then click Calculate. decimal places. The regular dodecahedron is a Platonic solid. Edge length and radius have the same unit (e.g. meter), the area has this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit -1.