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The solid angle, Ω, at the vertex of a Platonic solid is given in terms of the dihedral angle by Ω = q θ − ( q − 2 ) π . {\displaystyle \Omega =q\theta -(q-2)\pi .\,} This follows from the spherical excess formula for a spherical polygon and the fact that the vertex figure of the polyhedron { p , q } is a regular q -gon.
The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid. There are also three regular star dodecahedra, which are constructed as stellations of the convex form. All of these have icosahedral symmetry, order 120.
The pressure on a pressure-temperature diagram (such as the water phase diagram shown above) is the partial pressure of the substance in question. A phase diagram in physical chemistry , engineering , mineralogy , and materials science is a type of chart used to show conditions (pressure, temperature, etc.) at which thermodynamically distinct ...
Important classes of convex polyhedra include the family of prismatoid, the Platonic solids, the Archimedean solids and their duals the Catalan solids, and the regular polygonal faces polyhedron. The prismatoids are the polyhedron whose vertices lie on two parallel planes and their faces are likely to be trapezoids and triangles. [ 18 ]
The path or series of states through which a system passes from an initial equilibrium state to a final equilibrium state [1] and can be viewed graphically on a pressure-volume (P-V), pressure-temperature (P-T), and temperature-entropy (T-s) diagrams. [2] There are an infinite number of possible paths from an initial point to an end point in a ...
The boiling point of water is the temperature at which the saturated vapor pressure equals the ambient pressure. Water supercooled below its normal freezing point has a higher vapor pressure than that of ice at the same temperature and is, thus, unstable. Calculations of the (saturation) vapor pressure of water are commonly used in meteorology.
In the following table, material data are given with a pressure of 611.7 Pa (equivalent to 0.006117 bar). Up to a temperature of 0.01 °C, the triple point of water, water normally exists as ice, except for supercooled water, for which one data point is tabulated here. At the triple point, ice can exist together with both liquid water and vapor.
Other than rhombic triacontahedron, it is one of two Catalan solids that each have the property that their isometry groups are edge-transitive; the other convex polyhedron classes being the five Platonic solids and the other two Archimedean solids: its dual polyhedron and icosidodecahedron. Denoting by a the edge length of a rhombic dodecahedron,