The hemicube, which might also be called the square hemiprism, is a simple solid that serves as an example of one of the two topological classes of convex hexahedron having 7 vertices and 11 edges (the other being the hemiobelisk). It can be constructed by truncating a cube via a plane passing through two opposite vertices of a space diagonal and two edge midpoints, as illustrated above. This form is a space-filling polyhedron, as can be seen by placing two oppositely oriented hemicubes face-to-face along their truncated face.
It is implemented in the Wolfram Language as PolyhedronData["Hemicube"].
The faces of the hemicube consist of 2 right triangles (with side lengths 1/2, 1, and 
) and 4 quadrilaterals (two of
which are unit squares and the other two of which are right
trapezoids with sides 1/2, base 1, and top of length 
).
Its skeleton is the hemicubical graph.
The mean cylindrical radius of a hemicube constructed from a unit cube is equal to 
, where 
is the universal
parabolic constant.
The canonical hemicube, illustrated above, consists of 2 isosceles triangles, 2 kites, and 2 trapezoids.
It is implemented in the Wolfram Language as PolyhedronData["CanonicalHemicube"].
