Snub cube

The beveled hexahedron (also called Cubus simus ) is a chiral polyhedron is one of the Archimedean solids. It is composed of 38 surfaces, namely 6 squares and 32 equilateral triangles together and has 24 corners and 60 edges. In each case, four triangles and a square form a corner of the room.

Each other in pairs opposite squares are parallel and mutually rotated by about 33 ° ( the axis of rotation passes through the face centers ). The following pictures show two mirror -image bevelled hexahedron.

Mirror variant 2

The dual bevelled to hexahedral body is the Pentagonikositetraeder.

Construction

• As the name suggests, this polyhedron is produced by continuously chamfering a hexahedron, so that at the end of six (smaller) squares remain, which are coincident with the original boundary surfaces of the cube.

• By placing small pyramids ( with pentagonal base and four equilateral triangles and a " half square " than the face) to the eight pentagonal boundary surfaces of a special decahedron ( see right ) also obtained a sloping hexahedron.

• You Twisted at a Rhombicuboctahedron those six squares that are coincident with the boundary surfaces of a circumscribed cube ( and in pairs opposite ), against each other by the angle ω ( see formula below) and adds one diagonal in the other, now distorted squares, creates a sloping hexahedron.

Formulas

Below denote the term t the cosine of the smaller central angle ζ in Sehnenfünfeck ( the white lines in the graph on the right ) with side lengths a and d (square inch).

Used to double the value of t is the number 1 is added, we get the Tribonacci constant, which represents the limit of the ratio ( ≈ 1.84 ) of two consecutive numbers of this sequence.