Hexahedron

A hexahedron (plural: hexahedra) is any polyhedron with six faces. A cube, for example, is a regular hexahedron with all its faces square, and three squares around each vertex.

There are seven topologically distinct convex hexahedra,Counting polyhedra one of which exists in two mirror image forms. (Two polyhedra are "topologically distinct" if they have intrinsically different arrangements of faces and vertices, such that it is impossible to distort one into the other simply by changing the lengths of edges or the angles between edges or faces.)

Quadrilaterally-faced hexahedron (Cuboid) 6 faces, 12 edges, 8 vertices110px110px110px110px110px110px110pxCube(square)Rectangular cuboid(three pairs ofrectangles)Trigonal trapezohedron(congruent rhombi)Trigonal trapezohedron(congruent quadrilaterals)Quadrilateral frustum(apex-truncatedsquare pyramid)Parallelepiped(three pairs ofparallelograms)(three pairs ofrhombi)Oh, [4,3], (*432)order 48D2h, [2,2], (*222)order 8D3d, [2+,6], (2*3)order 12D3, [2,3]+, (223)order 6C4v, [4], (*44)order 8Ci, [2+,2+], (×)order 2
+ Others 100pxTriangular bipyramid36 Faces9 E, 5 V 75px75px Tetragonal antiwedge. Chiral – exists in "left-handed" and "right-handed" mirror image forms.4.4.3.3.3.3 Faces10 E, 6 V 100px4.4.4.4.3.3 Faces11 E, 7 V 100pxPentagonal pyramid5.35 Faces10 E, 6 V 100px5.4.4.3.3.3 Faces11 E, 7 V 100px5.5.4.4.3.3 Faces12 E, 8 V

There are three further topologically distinct hexahedra that can only be realised as concave figures:

 Concave 100px4.4.3.3.3.3 Faces10 E, 6 V 100px5.5.3.3.3.3 Faces11 E, 7 V 100px6.6.3.3.3.3 Faces12 E, 8 V

Related pages
Prismatoid

References

Other websites
Polyhedra with 4-7 Faces  by Steven Dutch

Category:Polyhedra