Since it has 8 faces, it is an octahedron. However, the term octahedron is primarily used to refer to the regular octahedron, which has eight triangular faces. Because of the ambiguity of the term octahedron and tilarity of the various eight-sided figures, the term is rarely used without clarification.
Before sharpening, many pencils take the shape of a long hexagonal prism.[2]
As in most prisms, the volume is found by taking the area of the base, with a side length of , and multiplying it by the height , giving the formula:[3]
and its surface area can be
.
Symmetry
The topology of a uniform hexagonal prism can have geometric variations of lower symmetry, 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. For p > 6, they are tilings of the hyperbolic plane, starting with the truncated triheptagonal tiling.
*n32 symmetry mutation of omnitruncated tilings: 4.6.2n