The rhombic dodecahedron is not regular, for though the lines and surfaces are equal, the angles are not.
Two of these generate the cube and the octahedron; five of these generate the dodecahedron and the icosahedron.
Thus we have a regular sequence of the platonic solids, and the question suggests itself, will further evolution develop elements shaped to the dodecahedron and the icosahedron?
Iamblichus here refers to thedodecahedron inscribed in the sphere.
Now, if the points of intersection be joined, a Dodecahedron is formed within the Sphere.
The connection between an Icosahedron and a Dodecahedron is something very peculiar and interesting, though the figures seem to be so very dissimilar to each other.
The Greeks discovered that if a line be divided in extreme and mean proportion, then the whole line and the greater segment are the lengths of the edge of a cube and dodecahedron inscriptible in the same sphere.
The crystals are frequently twinned, the twin-axis coinciding with a triad axis; a rhombic dodecahedron so twinned (fig.
The rhomboidal-dodecahedron is therefore the most perfect crystal.
Earth has the Cube: Fire has the Pyramid: Water has the Octahedron: Air has the Icosahedron: and the Dodecahedronis the plan of the Universe itself.
The regular dodecahedron of geometry, contained by twelve regular pentagons, is not a possible form in crystals.
In the thermo-electrically positive crystals of pyrites the faces of the pentagonal dodecahedron are striated parallel to the cubic edges, whilst in the rarer negative crystals the faces are striated perpendicular to these edges.
The general form is the Tetrahedral pentagonal dodecahedron (fig.
This is called a dodecahedral plane of symmetry, being parallel to the face of the rhombic dodecahedron which truncates the edge a1a2 (compare fig.
Of the seven simple forms, the cube, rhombic dodecahedron and tetrakis-hexahedron are geometrically the same as before, though on actual crystals the faces will have different surface characters.
A drawing of a crystal showing a combination of the cube, octahedron and rhombic dodecahedron is shown in fig.
In attempting to explain the significance of a pentagonal stone dodecahedron with vestiges of figures on it found near Marietta, Ohio, Dr.
A cube would therefore be represented numerically by seven, a dodecahedron by thirteen.
Hence the regular polyhedra have as many positions of equilibrium as they have angles or sides, the icosahedron twenty, dodecahedron twelve, octahedron eight, cube six, tetrahedron four.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "dodecahedron" in a variety of sentences. We hope that you will now be able to make sentences using this word.
