Dodecahedron in a sentence

The compound of the small stellated dodecahedron and great dodecahedron looks outwardly the same as the small stellated dodecahedron, because the great dodecahedron is completely contained inside.

A cube can be inscribed in a dodecahedron so that each vertex of the cube is a vertex of the dodecahedron and each edge is a diagonal of one of the dodecahedron's faces; taking all such cubes gives rise to the regular compound of five cubes.

In Conway polyhedron notation it can be seen as gT, a gyro tetrahedron. : Rhombic dodecahedron Rhombic dodecahedron The rhombic dodecahedron is a zonohedron with twelve rhombic faces and octahedral symmetry.

He depicts the great dodecahedron and the great stellated dodecahedron - this second is slightly distorted, probably through errors in method rather than ignorance of the form.

Rest assured, the Sophos Naked Security Dodecahedron of Code (or for short) is no ordinary D12.

A huge dodecahedron, in perspective so that edges appear in golden ratio to one another, is suspended above and behind Jesus and dominates the composition.

As it turns out, the icosahedron occupies less of the sphere's volume (60.54%) than the dodecahedron (66.49%).

Crystal habit Dodecahedron - shaped crystals from Italy.

For example, the small stellated dodecahedron has 12 pentagram faces with the central pentagonal part hidden inside the solid.

For this reason, the image shown above shows the small stellated dodecahedron in wireframe.

Geometric freedom The pyritohedron has a geometric degree of freedom with limiting cases of a cubic convex hull at one limit of colinear edges, and a rhombic dodecahedron as the other limit as 6 edges are degenerated to length zero.

Hamilton also invented " icosian calculus ", which he used to investigate closed edge paths on a dodecahedron that visit each vertex exactly once.

He also assembled convex polygons around star vertices to discover two more regular stars, the great icosahedron and great dodecahedron.

He noticed that by extending the edges or faces of the convex dodecahedron until they met again, he could obtain star pentagons.

If these square pyramids are then attached to the faces of a second cube, a rhombic dodecahedron is obtained (with pairs of coplanar triangles combined into rhombic faces).

In this example the size of the vertex figure was chosen so that its circumcircle lies on the intersphere of the cuboctahedron, which also becomes the intersphere of the dual rhombic dodecahedron.

Its occurrence in regular pentagons and decagons was duly observed, as well as in the dodecahedron (a regular polyhedron whose twelve faces are regular pentagons).

Note the duality between the cube and the octahedron, and between the dodecahedron and the icosahedron.

Of the fifth Platonic solid, the dodecahedron, Plato obscurely remarks, ".

One of the forms, called the pyritohedron (named for the group of minerals of which it is typical) has twelve pentagonal faces, arranged in the same pattern as the faces of the regular dodecahedron.