Ad
related to: 5 platonic shapes of matter chart for class 8 sciencegenerationgenius.com has been visited by 10K+ users in the past month
- Loved by Teachers
Check out some of the great
feedback from teachers & parents.
- Grades K-2 Science Videos
Get instant access to hours of fun
standards-based K-2 videos & more.
- Loved by Teachers
Search results
Results from the WOW.Com Content Network
In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges congruent), and the same number of faces meet at each vertex. There are only five such polyhedra:
Around the same time as the Pythagoreans, Plato described a theory of matter in which the five elements (earth, air, fire, water and spirit) each comprised tiny copies of one of the five regular solids. Matter was built up from a mixture of these polyhedra, with each substance having different proportions in the mix.
Able to conform to the shape of its container but retains a (nearly) constant volume independent of pressure. Gas: A compressible fluid. Not only will a gas take the shape of its container but it will also expand to fill the container. Mesomorphic states: States of matter intermediate between solid and liquid.
It can also be found in nature and supramolecules, as well as the shape of the universe. The skeleton of a regular dodecahedron can be represented as the graph called the dodecahedral graph, a Platonic graph. Its property of the Hamiltonian, a path visits all of its vertices exactly once, can be found in a toy called icosian game.
The elements of a polytope can be considered according to either their own dimensionality or how many dimensions "down" they are from the body.
The above shapes may also be realized as slices orthogonal to the long diagonal of a tesseract. If this diagonal is oriented vertically with a height of 1, then the first five slices above occur at heights r , 3 / 8 , 1 / 2 , 5 / 8 , and s , where r is any number in the range 0 < r ≤ 1 / 4 , and s is any number ...
The graphs of the Platonic solids have been called Platonic graphs. As well as having all the other properties of polyhedral graphs, these are symmetric graphs, and all of them have Hamiltonian cycles. [9] There are five of these graphs: Tetrahedral graph – 4 vertices, 6 edges; Octahedral graph – 6 vertices, 12 edges
Similarly, a k-isohedral tiling has k separate symmetry orbits (it may contain m different face shapes, for m = k, or only for some m < k). [ 6 ] ("1-isohedral" is the same as "isohedral".) A monohedral polyhedron or monohedral tiling ( m = 1) has congruent faces, either directly or reflectively, which occur in one or more symmetry positions.
Ad
related to: 5 platonic shapes of matter chart for class 8 sciencegenerationgenius.com has been visited by 10K+ users in the past month