3-4 duoprism

In geometry of 4 dimensions, a 3-4 duoprism, the second smallest p-q duoprism, is a 4-polytope resulting from the Cartesian product of a triangle and a square.

Uniform 3-4 duoprisms Schlegel diagrams
Type	Prismatic uniform polychoron
Schläfli symbol	{3}×{4}
Coxeter-Dynkin diagram
Cells	3 square prisms, 4 triangular prisms
Faces	3+12 squares, 4 triangles
Edges	24
Vertices	12
Vertex figure	Digonal disphenoid
Symmetry	[3,2,4], order 48
Dual	3-4 duopyramid
Properties	convex, vertex-uniform

The 3-4 duoprism exists in some of the uniform 5-polytopes in the B5 family.

Images

Net	3D projection with 3 different rotations
Skew orthogonal projections with primary triangles and squares colored

Related complex polygons

Stereographic projection of complex polygon, ₃{}×₄{} has 12 vertices and 7 3-edges, shown here with 4 red triangular 3-edges and 3 blue square 4-edges.

The quasiregular complex polytope ₃{}×₄{}, , in ${\displaystyle \mathbb {C} ^{2}}$ has a real representation as a 3-4 duoprism in 4-dimensional space. It has 12 vertices, and 4 3-edges and 3 4-edges. Its symmetry is ₃[2]₄, order 12.^[1]

Related polytopes

The birectified 5-cube, has a uniform 3-4 duoprism vertex figure:

3-4 duopyramid

3-4 duopyramid
Type	duopyramid
Schläfli symbol	{3}+{4}
Coxeter-Dynkin diagram
Cells	12 digonal disphenoids
Faces	24 isosceles triangles
Edges	19 (12+3+4)
Vertices	7 (3+4)
Symmetry	[3,2,4], order 48
Dual	3-4 duoprism
Properties	convex, facet-transitive

The dual of a 3-4 duoprism is called a 3-4 duopyramid. It has 12 digonal disphenoid cells, 24 isosceles triangular faces, 12 edges, and 7 vertices.

Orthogonal projection

Vertex-centered perspective

See also

• Polytope and polychoron
• Convex regular polychoron
• Duocylinder
• Tesseract