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Similarly, a k-isohedral tiling has k separate symmetry orbits (it may contain m different face shapes, for m = k, or only for some m < k). [ 6 ] ("1-isohedral" is the same as "isohedral".) A monohedral polyhedron or monohedral tiling ( m = 1) has congruent faces, either directly or reflectively, which occur in one or more symmetry positions.
Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result. The others are experimental, meaning that there is a difficulty in creating an experiment to test a proposed theory or investigate a phenomenon in greater detail.
This article is a list of notable unsolved problems in astronomy. Problems may be theoretical or experimental. Theoretical problems result from inability of current theories to explain observed phenomena or experimental results. Experimental problems result from inability to test or investigate a proposed theory.
The problem of anisohedral tiling has been generalised by saying that the isohedral number of a tile is the lowest number orbits (equivalence classes) of tiles in any tiling of that tile under the action of the symmetry group of that tiling, and that a tile with isohedral number k is k-anisohedral.
A state of matter is also characterized by phase transitions. A phase transition indicates a change in structure and can be recognized by an abrupt change in properties. A distinct state of matter can be defined as any set of states distinguished from any other set of states by a phase transition.
A stationary state is a quantum state with all observables independent of time. It is an eigenvector of the energy operator (instead of a quantum superposition of different energies). It is also called energy eigenvector , energy eigenstate , energy eigenfunction , or energy eigenket .
This shape is called a plesiohedron. The tiling generated in this way is isohedral, meaning that it not only has a single prototile ("monohedral") but also that any copy of this tile can be taken to any other copy by a symmetry of the tiling. [1] As with any space-filling polyhedron, the Dehn invariant of a plesiohedron is necessarily zero. [3]
Application of Stefan problem to metal crystallization in electrochemical deposition of metal powders was envisaged by Călușaru [13] The Stefan problem also has a rich inverse theory; in such problems, the melting depth (or curve or hyper-surface) s is the known datum and the problem is to find u or f. [14]