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  2. Platonic solid - Wikipedia

    en.wikipedia.org/wiki/Platonic_solid

    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 ...

  3. Dodecahedron - Wikipedia

    en.wikipedia.org/wiki/Dodecahedron

    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.

  4. Theory of forms - Wikipedia

    en.wikipedia.org/wiki/Theory_of_forms

    Plato distinguished between real and non-real "existing things", where the latter term is used of substance. The figures that the artificer places in the gold are not substance, but gold is. Aristotle stated that, for Plato, all things studied by the sciences have Form and asserted that Plato considered only substance to have Form.

  5. Dodecahedrane - Wikipedia

    en.wikipedia.org/wiki/Dodecahedrane

    The newly formed ketone group then forms another C–C bond by photochemical Norrish reaction to 19 whose alcohol group is induced to eliminate with TsOH to alkene 20. Dodecahedrane synthesis part V The double bond is reduced with hydrazine and sequential diisobutylaluminum hydride reduction and pyridinium chlorochromate oxidation of 21 forms ...

  6. Regular polyhedron - Wikipedia

    en.wikipedia.org/wiki/Regular_polyhedron

    Around the same time as the Pythagoreans, Plato described a theory of matter in which the five elements (earth, air, fire, water and spirit) each comprised tiny copies of one of the five regular solids. Matter was built up from a mixture of these polyhedra, with each substance having different proportions in the mix.

  7. Compound of dodecahedron and icosahedron - Wikipedia

    en.wikipedia.org/wiki/Compound_of_dodecahedron...

    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.

  8. Tetrahedron - Wikipedia

    en.wikipedia.org/wiki/Tetrahedron

    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.

  9. Timaeus (dialogue) - Wikipedia

    en.wikipedia.org/wiki/Timaeus_(dialogue)

    The fifth element (i.e. Platonic solid) was the dodecahedron, whose faces are not triangular, and which was taken to represent the shape of the Universe as a whole, possibly because of all the elements it most approximates a sphere, which Timaeus has already noted was the shape into which God had formed the Universe. [9]