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The hypercubes are one of the few families of regular polytopes that are represented in any number of dimensions. [8] The hypercube (offset) family is one of three regular polytope families, labeled by Coxeter as γ n. The other two are the hypercube dual family, the cross-polytopes, labeled as β n, and the simplices, labeled as α n.
The two general forms of the hypercube honeycombs are the regular form with identical hypercubic facets and one semiregular, with alternating hypercube facets, like a checkerboard. A third form is generated by an expansion operation applied to the regular form, creating facets in place of all lower-dimensional elements.
In this tiling of the plane by congruent squares, the green and violet squares meet edge-to-edge as do the blue and orange squares. In geometry, Keller's conjecture is the conjecture that in any tiling of n-dimensional Euclidean space by identical hypercubes, there are two hypercubes that share an entire (n − 1)-dimensional face with each other.
Alternation of the n-cube yields one of two n-demicubes, as in this 3-dimensional illustration of the two tetrahedra that arise as the 3-demicubes of the 3-cube.. In geometry, demihypercubes (also called n-demicubes, n-hemicubes, and half measure polytopes) are a class of n-polytopes constructed from alternation of an n-hypercube, labeled as hγ n for being half of the hypercube family, γ n.
In polymer chemistry, polymerization (American English), or polymerisation (British English), is a process of reacting monomer molecules together in a chemical reaction to form polymer chains or three-dimensional networks. [1] [2] [3] There are many forms of polymerization [4] and different systems exist to categorize them. IUPAC definition for ...
In organic chemistry, a cross-coupling reaction is a reaction where two different fragments are joined. Cross-couplings are a subset of the more general coupling reactions. Often cross-coupling reactions require metal catalysts. One important reaction type is this:
Phase transitions (phase changes) that help describe polymorphism include polymorphic transitions as well as melting and vaporization transitions. According to IUPAC, a polymorphic transition is "A reversible transition of a solid crystalline phase at a certain temperature and pressure (the inversion point) to another phase of the same chemical composition with a different crystal structure."
Chemical energy is the energy that can be released when chemical substances undergo a transformation through a chemical reaction. Breaking and making chemical bonds involves energy release or uptake, often as heat that may be either absorbed by or evolved from the chemical system. Energy released (or absorbed) because of a reaction between ...