Jump to content

User:Tomruen/triaprism

From Wikipedia, the free encyclopedia
p-q-r prism
Type Uniform 6-polytope
Schläfli symbol {p}×{q}×{r}
Coxeter diagram
or
5-faces 9:
3 {p}×{q}×{ }
3 {p}×{r}×{ }
3 {q}×{r}×{ }
4-faces pq+pr+qr+p+q+r
Cells pqr+2(pq+pr+qr)
Faces 3pqr+pq+pr+qr
Edges 3pqr
Vertices pqr
Vertex figure 5-simplex = { }∨{ }∨{ }
Symmetry [p,2,q,2,r], order 8pqr
Dual p-q-r pyramid
Properties convex, vertex-uniform, facet-transitive

A triaprism is a 6-polytope constructed as the product of 3 orthogonal polygons.

A uniform triaprism is the product of three regular polygons, {p}×{q}×{r}, form an infinite class for all integers p,q,r>2.

The smallest triaprism is a 3-3-3 prism. {4}×{4}×{4} makes a lower symmetry form of the 6-cube.

A p-q-r prism is a real representation of the set of complex polytopes .

p-p-p prism
Type Uniform 6-polytope
Schläfli symbol {p}×{p}×{p} = {p}3
Coxeter diagram
or
5-faces 3p {p}×{p}×{ }
4-faces 3p2 {p}×{4}
3p {p}2
Cells 6p2 {p}×{ }
p3 {4}2
Faces 3p2 {p}
3p3 {4}
Edges 3p3
Vertices p3
Vertex figure 5-simplex = { }∨{ }∨{ }
Symmetry [3[p,2,p,2,p]], order 48p3
Dual p-p-p pyramid
Properties convex, vertex-uniform, facet-transitive

p-p-p prisms

[edit]

A p-p-p prism or p-gonal triple prism or p-gonal triaprism, {p}×{p}×{p} or {p}3, has extended symmetry [3[p,2,p,2,p]], order 48p3. A 4-4-4 prism is also a 6-cube, extends symmetry order from 3072 to 266! or 46080. Therefore [4]3 is an index 15 subgroup of [4,3,3,3,3].

A p-p-p prism is a real representation of the set of complex polytope generalized cubes .

Name {3}3 {4}3 {5}3 {6}3 {7}3 {8}3
Vertices 27 64 125 216 343 512
Edge 81 192 375 648 1029 1536
Symmetry
Order
1296 3072 6000 10364 16464 24576
Image

References

[edit]

See also

[edit]