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  1. History

    The Platonic solids have been known since antiquity. It has been suggested that certain carved stone balls created … See more

    Platonic solid - Wikipedia

    • In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges congruent), and the same number of faces meet at each vertex. There are only five such polyhedra: Geo… See more

    The Amazing Platonic Solids
    The Amazing Platonic Solids
     The Perfect 3D Shapes
    The Perfect 3D Shapes
    Combinatorial properties

    A convex polyhedron is a Platonic solid if and only if all three of the following requirements are met.
    • All of its faces are congruent convex regular polygons.
    • None of its faces intersect except at th… See more

    Classification

    The classical result is that only five convex regular polyhedra exist. Two common arguments below demonstrate no more than five Platonic solids can exist, but positively demonstrating the existence of any given s… See more

    Geometric properties

    There are a number of angles associated with each Platonic solid. The dihedral angle is the interior angle between any two face planes. The dihedral angle, θ, of the solid {p,q} is given by the formula
    This is som… See more

    Symmetry

    Every polyhedron has a dual (or "polar") polyhedron with faces and vertices interchanged. The dual of every Platonic solid is another Platonic solid, so that we can arrange the five solids into dual pairs.
    • The … See more

    In nature and technology

    The tetrahedron, cube, and octahedron all occur naturally in crystal structures. These by no means exhaust the numbers of possible forms of crystals. However, neither the regular icosahedron nor the regular dodecahed… See more

    In architecture

    Architects liked the idea of Plato's timeless forms that can be seen by the soul in the objects of the material world, but turned these shapes into more suitable for construction sphere, cylinder, cone, and square pyr… See more

     
  1. Convex, regular polyhedron in three-dimensional Euclidean space

    In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges congruent), and the same number of faces meet at each vertex.
    en.wikipedia.org/wiki/Platonic_solid
    en.wikipedia.org/wiki/Platonic_solid
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