Search results
Results from the WOW.Com Content Network
The Platonic solids have been known since antiquity. It has been suggested that certain carved stone balls created by the late Neolithic people of Scotland represent these shapes; however, these balls have rounded knobs rather than being polyhedral, the numbers of knobs frequently differed from the numbers of vertices of the Platonic solids, there is no ball whose knobs match the 20 vertices ...
The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid. There are also three regular star dodecahedra, which are constructed as stellations of the convex form. All of these have icosahedral symmetry, order 120.
A regular polyhedron is identified by its Schläfli symbol of the form {n, m}, where n is the number of sides of each face and m the number of faces meeting at each vertex. There are 5 finite convex regular polyhedra (the Platonic solids), and four regular star polyhedra (the Kepler–Poinsot polyhedra), making nine regular polyhedra in all. In ...
Expansion involves moving each face away from the center (by the same distance to preserve the symmetry of the Platonic solid) and taking the convex hull. An example is the rhombicuboctahedron, constructed by separating the cube or octahedron's faces from the centroid and filling them with squares. [ 8 ]
It can be seen as the compound of an icosahedron and dodecahedron.It is one of four compounds constructed from a Platonic solid or Kepler-Poinsot solid, and its dual.. It has icosahedral symmetry (I h) and the same vertex arrangement as a rhombic triacontahedron.
In the Timaeus, his major cosmological dialogue, the Platonic solid associated with water is the icosahedron which is formed from twenty equilateral triangles. This makes water the element with the greatest number of sides, which Plato regarded as appropriate because water flows out of one's hand when picked up, as if it is made of tiny little ...
Pages in category "Platonic solids" The following 10 pages are in this category, out of 10 total. This list may not reflect recent changes. ...
The regular tetrahedron is also one of the five regular Platonic solids, a set of polyhedrons in which all of their faces are regular polygons. [4] Known since antiquity, the Platonic solid is named after the Greek philosopher Plato , who associated those four solids with nature.