Octahedron Geometry

Any cubic crystal structure can be divided into small units in the form of congruent semi-regular (Archimedean) truncated octahedra. The centers of these polyhedra can be chosen at invariant equivalent positions for most cubic space groups. The part of a crystal structure enclosed by an Archimedean polyhedron is called a geometric unit (or unit for short); however, the boundary of the unit may be relaxed to include a whole molecule or ion in case the geometric division is not convenient.

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Based on the properties and arrangements of such geometric units, there is an interesting relationship among the 36 cubic space groups. All units in a crystal structure of any one of 16 space groups are equivalent. There are 14 space groups to accommodate crystal structures with two types of independent units. Only crystal structures of space groups F23 and F 3 m consist of four types of independent units.

The remaining four space groups are in the class with three types of geometric units. The arrangement of geometric units is represented by a sequence of one period along the body diagonals of a unit cell. The sequence of geometric units is a simple version of the packing map on a (110) plane. This packing map reveals structural features.

The ancient Greek philosopher Plato c. Theorized that the classical elements of the world were made of these regular solids. The five Platonic Solids were thought to represent the five basic elements: earth, air, fire, water, and the universe. The cube is associated with the earth, and reconnecting energy to nature. The octahedron is associated with air, and cultivating acceptance and compassion. The tetrahedron is associated with fire, and perpetuates balance and stability.

Octahedral molecular geometry describes the shape of compounds wherein six atoms or groups of atoms or ligands are symmetrically arranged around a central atom. The octahedron has eight faces, hence the prefix octa. An octahedron is a regular geometric solid (called a Platonic solid) that has a 8 equilateral triangles as faces. Caesar ii free download full version. It has 6 vertices (points) and 12 edges (lines.

The icosahedron is associated with water, and enhances creative though and expression. The dodecahedron is associated with the universe, and represents mystery and meditation. Plato stated that the dodecahedron was 'used for arranging the constellations on the whole heaven.' The dodecahedron can be seen as representing the universe with the twelve zodiac signs corresponding to the twelve faces of the dodecahedron.These regular solids occur in areas such as chemistry, crystallography, mineralogy, oceanography, medical virology, cytology (the study of cells), geology, meteorology, astrology, electronics, and architecture, to name only a few. The Platonic solids can be described as forming the basis of all structure.

A soccer ball is composed of a combination of pentagon and hexagon faces. This shape is called a buckyball after Richard Buckminster Fuller, who patented the geodesic dome. In reality, the soccer ball is not truly a polyhedron since the faces are not really flat. The faces tend to bulge slightly due to the amount of stuffing in the ball and the pliable nature of the leather. A buckyball is actually a spherical molecule whose structure resembles a truncated icosahedron with twenty hexagons and twelve pentagons.