What is "hemicube"

n. (context geometry English) An abstract regular polyhedron containing half the faces of a cube.

In 3D computer graphics rendering, a hemicube is one way to represent a 180° view from a surface or point in space.

In abstract geometry, a hemicube is an abstract regular polyhedron, containing half the faces of a cube.

It can be realized as a projective polyhedron (a tessellation of the real projective plane by three quadrilaterals), which can be visualized by constructing the projective plane as a hemisphere where opposite points along the boundary are connected and dividing the hemisphere into three equal parts.

It has three square faces, six edges, and four vertices. It has an unexpected property that every face is in contact with every other face on two edges, and every face contains all the vertices, which gives an example of an abstract polytope whose faces are not determined by their vertex sets.

From the point of view of graph theory the skeleton is a tetrahedral graph, an embedding of K (the complete graph with four vertices) on a projective plane.

The hemicube should not be confused with the demicube – the hemicube is a projective polyhedron, while the demicube is an ordinary polyhedron (in Euclidean space). While they both have half the vertices of a cube, the hemicube is a quotient of the cube, while the vertices of the demicube are a subset of the vertices of the cube.

Hemicube can mean:

• Hemicube (computer graphics), a concept in 3D computer graphics rendering
• Hemicube (geometry), an abstract regular polytope
• Demihypercube, an n-dimensional uniform polytope, also known as the n-hemicube