Hexagonal prism

Before sharpening, many pencils take the shape of a long hexagonal prism.

[2] If faces are all regular, the hexagonal prism is a semiregular polyhedron, more generally, a uniform polyhedron, and the fourth in an infinite set of prisms formed by square sides and two regular polygon caps.

It can be seen as a truncated hexagonal hosohedron, represented by Schläfli symbol t{2,6}.

The symmetry group of a right hexagonal prism is D6h of order 24.

As in most prisms, the volume is found by taking the area of the base, with a side length of

The topology of a uniform hexagonal prism can have geometric variations of lower symmetry, including: It exists as cells of four prismatic uniform convex honeycombs in 3 dimensions: It also exists as cells of a number of four-dimensional uniform 4-polytopes, including: This polyhedron can be considered a member of a sequence of uniform patterns with vertex figure (4.6.2p) and Coxeter-Dynkin diagram .

For p < 6, the members of the sequence are omnitruncated polyhedra (zonohedrons), shown below as spherical tilings.