Hemicube

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 sqrt(5)/2) 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 sqrt(5)/2).

Its skeleton is the hemicubical graph.

The mean cylindrical radius of a hemicube constructed from a unit cube is equal to 8P/3, where P 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"].

See also

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References

Referenced on Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Hemicube." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Hemicube.html

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