3-8 duoprism

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.

Uniform 3-8 duoprisms

Schlegel diagrams
TypePrismatic uniform polychoron
Schläfli symbol{3}×{8}
{3}×t{4}
Coxeter diagram
Cells3 octagonal prisms,
8 triangular prisms
Faces24 squares,
3 octagons,
8 triangles
Edges48
Vertices24
Vertex figureDigonal disphenoid
Symmetry[3,2,8], order 48
Dual3-8 duopyramid
Propertiesconvex, vertex-uniform

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

Images


Net

3-8 duopyramid

3-8 duopyramid
Typeduopyramid
Schläfli symbol{3}+{8}
{3}+t{4}
Coxeter-Dynkin diagram
Cells24 digonal disphenoids
Faces48 isosceles triangles
Edges35 (24+3+8)
Vertices11 (3+8)
Symmetry[3,2,8], order 48
Dual3-8 duoprism
Propertiesconvex, 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.


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.


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