3-8 duoprism

From HandWiki
Uniform 3-8 duoprisms
3-8 duoprism.png 140px
Schlegel diagrams
Type Prismatic uniform polychoron
Schläfli symbol {3}×{8}
{3}×t{4}
Coxeter diagram CDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 8.pngCDel node.png
CDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node 1.png
Cells 3 octagonal prisms,
8 triangular prisms
Faces 24 squares,
3 octagons,
8 triangles
Edges 48
Vertices 24
Vertex figure Digonal disphenoid
Symmetry [3,2,8], order 48
Dual 3-8 duopyramid
Properties convex, vertex-uniform

In geometry of 4 dimensions, a 3-8 duoprism, a duoprism and 4-polytope resulting from the Cartesian product of a triangle and an octagon.

The 3-8 duoprism exists in some of the uniform 5-polytopes in the B5 family.

Images

3-8 duoprism net.png
Net

3-8 duopyramid

3-8 duopyramid
Type duopyramid
Schläfli symbol {3}+{8}
{3}+t{4}
Coxeter-Dynkin diagram CDel node f1.pngCDel 3.pngCDel node.pngCDel 2x.pngCDel node f1.pngCDel 8.pngCDel node.png
CDel node f1.pngCDel 3.pngCDel node.pngCDel 2x.pngCDel node f1.pngCDel 4.pngCDel node f1.png
Cells 24 digonal disphenoids
Faces 48 isosceles triangles
Edges 35 (24+3+8)
Vertices 11 (3+8)
Symmetry [3,2,8], order 48
Dual 3-8 duoprism
Properties convex, facet-transitive

The dual of a 3-8 duoprism is called a 3-8 duopyramid. It has 24 digonal disphenoid cells, 48 isosceles triangular faces, 35 edges, and 11 vertices.

3-8 duopyramid ortho.png
Orthogonal projection

See also

Notes

References

  • Regular Polytopes, H. S. M. Coxeter, Dover Publications, Inc., 1973, New York, p. 124.
  • Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999, ISBN:0-486-40919-8 (Chapter 5: Regular Skew Polyhedra in three and four dimensions and their topological analogues)
    • Coxeter, H. S. M. Regular Skew Polyhedra in Three and Four Dimensions. Proc. London Math. Soc. 43, 33–62, 1937.
  • John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN:978-1-56881-220-5 (Chapter 26)
  • Norman Johnson Uniform Polytopes, Manuscript (1991)
    • N. W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. Dissertation, University of Toronto, 1966
  • Catalogue of Convex Polychora, section 6, George Olshevsky.

External links