Ads
related to: platonic solid symmetry formula worksheet gradeteacherspayteachers.com has been visited by 100K+ users in the past month
- Worksheets
All the printables you need for
math, ELA, science, and much more.
- Projects
Get instructions for fun, hands-on
activities that apply PK-12 topics.
- Resources on Sale
The materials you need at the best
prices. Shop limited time offers.
- Packets
Perfect for independent work!
Browse our fun activity packs.
- Worksheets
Search results
Results from the WOW.Com Content Network
The symmetry groups of the Platonic solids are a special class of three-dimensional point groups known as polyhedral groups. The high degree of symmetry of the Platonic solids can be interpreted in a number of ways. Most importantly, the vertices of each solid are all equivalent under the action of the symmetry group, as are the edges and faces.
Each convex regular 4-polytope is bounded by a set of 3-dimensional cells which are all Platonic solids of the same type and size. These are fitted together along their respective faces (face-to-face) in a regular fashion, forming the surface of the 4-polytope which is a closed, curved 3-dimensional space (analogous to the way the surface of ...
All five have C 2 ×S 5 symmetry but can only be realised with half the symmetry, that is C 2 ×A 5 or icosahedral symmetry. [9] [10] [11] They are all topologically equivalent to toroids. Their construction, by arranging n faces around each vertex, can be repeated indefinitely as tilings of the hyperbolic plane. In the diagrams below, the ...
It follows that all vertices are congruent, and the polyhedron has a high degree of reflectional and rotational symmetry. Uniform polyhedra can be divided between convex forms with convex regular polygon faces and star forms. Star forms have either regular star polygon faces or vertex figures or both. This list includes these:
The tetrahedron is the only Platonic solid not mapped to itself by point inversion. The proper rotations, (order-3 rotation on a vertex and face, and order-2 on two edges) and reflection plane (through two faces and one edge) in the symmetry group of the regular tetrahedron
The convex regular 4-polytopes are the four-dimensional analogues of the Platonic solids. The most familiar 4-polytope is the tesseract or hypercube, the 4D analogue of the cube. The convex regular 4-polytopes can be ordered by size as a measure of 4-dimensional content (hypervolume) for the same radius.
Ads
related to: platonic solid symmetry formula worksheet gradeteacherspayteachers.com has been visited by 100K+ users in the past month