In 4-dimensional

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...

, the cuboctahedral pyramid is bounded by one

cuboctahedron A cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces. A cuboctahedron has 12 identical vertices, with 2 triangles and 2 squares meeting at each, and 24 identical edges, each separating a triangle from a square. As such, it ...

on the base, 6 square pyramid, and 8 triangular pyramid cells which meet at the apex. It has 38 faces: 32

triangles A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear ...

and 6

square In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90- degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length a ...

s. It has 32 edges, and 13 vertices. Since a cuboctahedron's circumradius is equal to its edge length, the triangles must be taller than equilateral to create a positive height. The dual to the cuboctahedral pyramid is a ''rhombic dodecahedral pyramid'', seen as a rhombic dodecahedral base, and 12 rhombic pyramids meeting at an apex. :

References

External links

* * Richard Klitzing
Axial-Symmetrical Edge Facetings of Uniform Polyhedra
4-polytopes {{Polychora-stub