What are the angles 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….
| Regular dodecahedron | |
|---|---|
| Dihedral angle | 116.56505° = arccos(−1⁄√5) |
| 5.5.5 (Vertex figure) | Regular icosahedron (dual polyhedron) |
| Net |
How many points does a great Stellated dodecahedron have?
12
It is one of four nonconvex regular polyhedra. It is composed of 12 intersecting pentagrammic faces, with three pentagrams meeting at each vertex….
| Great stellated dodecahedron | |
|---|---|
| Properties | Regular nonconvex |
| ( 5⁄2)3 (Vertex figure) | Great icosahedron (dual polyhedron) |
How many triangles are in a great dodecahedron?
The Great Dodecahedron is one of the four Kepler-Poinsot Polyhedra. The 12 faces of the Great Dodecahedron are made out of 5 triangles each. The model is made out of 60 parts of faces.
How do you find the angle of a dodecahedron?
In this case there is a convenient formula for calculating the dihedral angle. In a dodecahedron, all of the angles, a, b, g, are equal and are 108 degrees. This is due to the fact that each of the faces is a regular pentagon and in a regular pentagon each angle is , where n is 5. and so q = 116.57 degrees.
How many triangles are in a stellated dodecahedron?
60 triangles
The stellated dodecahedron is made up of 20 tips with 3 isosceles triangles in each tips for a total of 60 triangles. Compare these numbers to those of the stellated dodecahedron. You’ll really start to see why the dodecahedron and the icosahedron are duals!
How many bases does dodecahedron have?
twelve
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.
