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Rotating model of the diamond cubic crystal structure 3D ball-and-stick model of a diamond lattice Pole figure in stereographic projection of the diamond lattice showing the 3-fold symmetry along the [111] direction. In crystallography, the diamond cubic crystal structure is a repeating pattern of 8 atoms that certain materials may adopt as ...
Cubic boron nitride adopts a sphalerite crystal structure, which can be constructed by replacing every two carbon atoms in diamond with one boron atom and one nitrogen atom. The short B-N (1.57 Å) bond is close to the diamond C-C bond length (1.54 Å), that results in strong covalent bonding between atoms in the same fashion as in diamond.
Diamond is extremely strong owing to its crystal structure, known as diamond cubic, in which each carbon atom has four neighbors covalently bonded to it. Bulk cubic boron nitride (c-BN) is nearly as hard as diamond. Diamond reacts with some materials, such as steel, and c-BN wears less when cutting or abrading such material. [4]
Its diamond structure can be considered to be made up of interlocking rings of six carbon atoms, in the chair conformation. In lonsdaleite, some rings are in the boat conformation instead. At nanoscale dimensions, cubic diamond is represented by diamondoids while hexagonal diamond is represented by wurtzoids. [10]
Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world.
The convex regular 4-polytopes were first described by the Swiss mathematician Ludwig Schläfli in the mid-19th century. [1] He discovered that there are precisely six such figures. Schläfli also found four of the regular star 4-polytopes: the grand 120-cell, great stellated 120-cell, grand 600-cell, and great grand stellated 120-cell.
[2] [3] [4] The factor–label method is the sequential application of conversion factors expressed as fractions and arranged so that any dimensional unit appearing in both the numerator and denominator of any of the fractions can be cancelled out until only the desired set of dimensional units is obtained.
In four-dimensional Euclidean geometry, the 16-cell honeycomb is one of the three regular space-filling tessellations (or honeycombs), represented by Schläfli symbol {3,3,4,3}, and constructed by a 4-dimensional packing of 16-cell facets, three around every face. Its dual is the 24-cell honeycomb. Its vertex figure is a 24-cell.
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