Small rhombicuboctaèdre

The small rhombicuboctaèdre is a Solide of Archimedes with eight triangular faces and eighteen square faces . There exist 24 identical tops, with a triangle and three squares meeting there. Note : six of the squares share only the tops with the triangles whereas the twelve others divide an edge. The Polyèdre has a octahedral Symétrie, like the Cube and the Octaèdre. Its dual is called the trapezoidal Icositétraèdre, although its faces are not really of truths Trapèze S.

The name rhombicuboctaèdre refers to the fact that 12 of the square faces are placed in the same plans as the 12 faces of the rhombic Dodécaèdre which is dual Cuboctaèdre.

It can also be called a wide cube or octahedral wide starting from the operations of truncations of the Polyèdre uniform.

The Cartesian coordinated for a rhombicuboctaèdre are all the permutations of

(\ pm1, \ pm1, \ pm (1+ \ sqrt {2}))\,

There exist three pairs of parallel plans which cut each one the rhombicuboctaèdre through eight edges taking the shape of a regular octagone. The rhombicuboctaèdre can be divided along two unspecified to obtain an octagonal prism with regular faces and two additional polyhedrons called square cupolas, which appear among the solid of Johnson. Those can be gathered to give a new solid called the pseudorhombicuboctaèdre (or bicoupole square gyroallongée) with the symmetry of a square antiprism. In this one, the tops all are locally the same ones as those of the rhombicuboctaèdre, with a triangle and three squares meeting at each top, but are not all identical with regard to the whole polyhedron, since some are more close to the axis of symmetry than of others.

There exist distortions of small the rhombicuboctaèdre such as, whereas some faces are not regular polygons, they are still uniform by the tops. Some of those can be made by taking a cube or octahedral and by cutting out the edges, then by balancing the corners, thus the resulting polyhedron has six rectangular squares and twelve faces. Those have an octahedral symmetry and forms a series continues between the cube and octahedral, similar to the distortions of the small one the rhombicosidodécaèdre or the tetrahedral distortions of the Cuboctaèdre. Nevertheless, small the rhombicuboctaèdre has also a second whole of distortions with six rectangular faces and sixteen trapezoidal faces, which do not have symmetry octahedral but rather a Th symmetry, therefore, they are invariants under same rotations that the Tétraèdre but have different reflections.

The lines the length whose a Rubik' S Cubes can be turned, are projected on a sphere, similar, topologically identical to the edges of small a rhombicuboctaèdre. In fact, the alternatives using the mechanism of Rubik' S Cube were produced, resembling of close with small the rhombicuboctaèdre.

Small the rhombicuboctaèdre is a space filled by a combination of cubes and tetrahedrons.

The rhombicuboctaèdre in arts

The polyhedron in the portrait of Luca Pacioli is small a rhombicuboctaèdre of glass to half filled with water.

See too

  • the Cubic
  • the Cuboctaèdre
  • the Octahedral
  • the rhombicosidodécaèdre
  • the Large rhombicuboctaèdre
  • the square Gyrobicoupole lengthened
  • the Rubik' S Snake - a puzzle which can form a " boule" rhombicuboctaedric

References

  • Robert Williams, The Geometrical Foundation off Natural Structure: With Book Source off Design, 1979, ISBN 0-486-23729-X

External bonds

  • Archimedes and Rhombicuboctaèdre by Antonio Gutierrez of Geometry Step by Step from the Land off the Incas .
  • uniform polyhedrons
  • polyhedrons actually virtual the encyclopedia of the Polyhedrons

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