How to use Dodecahedron in a sentence
The truncated dodecahedron is formed by truncating the vertices of a dodecahedron parallel to the faces of the coaxial icosahedron so as to leave the former decagons.
The pentagon is the basis of the dodecahedron.
It is enclosed by 20 triangular faces belonging to the icosahedron and 12 decagons belonging to the dodecahedron.
Shown above is an icosahedron of twelve dodecahedral structures surrounding a central dodecahedron; (H 2 O) 130.
Unfortunately, my magnetic kit didn't have enough connectors to make a dodecahedron, so here is a child's ball instead.Advertisement
The form of David Mitchell's Six-way Brick is a rhombic dodecahedron from which twelve small rhombic pyramids have been removed.
It is not actually a regular dodecahedron, although it has 12 faces, each with 5 sides, but it is quite close.
The triply periodic structure is generated by reflections in the faces of the rhombic dodecahedron.
The form of David Mitchell's Six-way Brick is a rhombic dodecahedron from which twelve small rhombic dodecahedron from which twelve small rhombic pyramids have been removed.
If it is evaporated slowly, anhydrous stannous oxide crystallizes out in forms which are combinations of the cube and dodecahedron.Advertisement
In crystallography the icosahedron is a possible form, but it has not been observed; it is closely simulated by a combination of the octahedron and pentagonal dodecahedron, which has twenty triangular faces, but only eight are equilateral, the remaining twelve being isosceles (see Crystallography).
The "ordinary dodecahedron" is one of the Platonic solids (see Polyhedron).
The "small stellated dodecahedron," the "great dodecahedron" and the "great stellated dodecahedron" are Kepler-Poinsot solids; and the "truncated" and "snub dodecahedra" are Archimedean solids (see Polyhedron).
It is the reciprocal (see below) of the small stellated dodecahedron.
The snub dodecahedron is a 92-faced solid having 4 triangles and a pentagon at each corner.Advertisement
Elie de Beaumont, in his speculations on the relation between the direction of mountain ranges and their geological age and character, was feeling towards a comprehensive theory of the forms of crustal relief; but his ideas were too geometrical, and his theory that the earth is a spheroid built up on a rhombic dodecahedron, the pentagonal faces of which determined the direction of mountain ranges, could not be proved.'
The "rhombic dodecahedron," one of the geometrical semiregular solids, is an important crystal form.
The great icosahedron is the reciprocal of the great stellated dodecahedron.
It is enclosed by 20 triangular faces belonging to the original icosahedron, and 12 pentagonal faces belonging to the coaxial dodecahedron.
It is therefore enclosed by 20 hexagonal faces belonging to the icosahedron, and 12 pentagonal faces belonging to the coaxial dodecahedron.Advertisement
Crystals of blende belong to that subclass of the cubic system in which there are six planes of symmetry parallel to the faces of the rhombic dodecahedron and none parallel to the cubic faces; in other words, the crystals are cubic with inclined hemihedrism, and have no centre of symmetry.
An important character of blende is the perfect dodecahedral cleavage, there being six directions of cleavage parallel to the faces of the rhombic dodecahedron, and angles between which are 600.
Percussionfigures, readily made on the cleavage-faces, have rays parallel to faces of the rhombic dodecahedron; whilst figures etched with water represent the four-faced cube.
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.
In crystallography, the regular or ordinary dodecahedron is an impossible form since the faces cut the axes in irrational ratios; the "pentagonal dodecahedron" of crystallographers has irregular pentagons for faces, while the geometrical solid, on the other hand, has regular ones.Advertisement
In the " small rhombicosidodecahedron " there are 12 pentagonal faces belonging to the dodecahedron, 20 triangular faces belonging to the icosahedron and 30 square faces belonging to the triacontahedron.
The pentagons belong to a dodecahedron, and 20 triangles to an icosahedron; the remaining 60 triangles belong to no regular solid.
The first three were certainly known to the Egyptians; and it is probable that the icosahedron and dodecahedron were added by the Greeks.
The small stellated dodecahedron is formed by stellating the Platonic dodecahedron (by "stellating " is meant developing the faces contiguous to a specified base so as to form a regular pyramid).
The great dodecahedron is determined by the intersections of the twelve planes which intersect the Platonic icosahedron in five of its edges; or each face has the same boundaries as the basal sides of five covertical faces of the icosahedron.Advertisement
The great stellated dodecahedron is formed by stellating the faces of a great dodecahedron.
African stones; and the dodecahedron is perhaps more common in Brazil than elsewhere.
Thus the faces of the cuboctahedron, the truncated cube, and truncated octahedron, correspond; likewise with the truncated dodecahedron, truncated icosahedron, and icosidodecahedron; and with the small and great rhombicosidodecahedra.
The rhombic faces of the dodecahedron are often striated parallel to the longer diagonal.
As examples of facial holohedra we may notice the small rhombicuboctahedron and rhombic dodecahedron, and the small rhombicosidodecahedron and the semiregular triacontahedron.Advertisement