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The Platonic solids have been known since antiquity. It has been suggested that certain carved stone balls created by the late Neolithic people of Scotland represent these shapes; however, these balls have rounded knobs rather than being polyhedral, the numbers of knobs frequently differed from the numbers of vertices of the Platonic solids, there is no ball whose knobs match the 20 vertices ...
A comparison between the five platonic solids and the corresponding three platonic hydrocarbons. In organic chemistry, a Platonic hydrocarbon is a hydrocarbon whose structure matches one of the five Platonic solids, with carbon atoms replacing its vertices, carbon–carbon bonds replacing its edges, and hydrogen atoms as needed. [1] [page needed]
A solid angle of π sr is one quarter of that subtended by all of space. When all the solid angles at the vertices of a tetrahedron are smaller than π sr, O lies inside the tetrahedron, and because the sum of distances from O to the vertices is a minimum, O coincides with the geometric median, M, of the vertices.
It can be seen as the compound of an icosahedron and dodecahedron.It is one of four compounds constructed from a Platonic solid or Kepler-Poinsot solid, and its dual.. It has icosahedral symmetry (I h) and the same vertex arrangement as a rhombic triacontahedron.
Cubane is a synthetic hydrocarbon compound with the formula C 8 H 8. It consists of eight carbon atoms arranged at the corners of a cube, with one hydrogen atom attached to each carbon atom. A solid crystalline substance, cubane is one of the Platonic hydrocarbons and a member of the prismanes.
Other than two Platonic solids—tetrahedron and cube—the regular dodecahedron is the initial of Goldberg polyhedron construction, and the next polyhedron is resulted by truncating all of its edges, a process called chamfer. This process can be continuously repeated, resulting in more new Goldberg's polyhedrons.
However, its first-generation solid-state batteries are less volatile, have better thermal resistance, and charge more quickly than traditional lithium-ion batteries.
There are 5 finite convex regular polyhedra (the Platonic solids), and four regular star polyhedra (the Kepler–Poinsot polyhedra), making nine regular polyhedra in all. In addition, there are five regular compounds of the regular polyhedra.