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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 ...
Truncated icosahedron, one of the Archimedean solids illustrated in De quinque corporibus regularibus. The five Platonic solids (the regular tetrahedron, cube, octahedron, dodecahedron, and icosahedron) were known to della Francesca through two classical sources: Timaeus, in which Plato theorizes that four of them correspond to the classical elements making up the world (with the fifth, the ...
The five convex regular polyhedra are called the Platonic solids. The vertex figure is given with each vertex count. All these polyhedra have an Euler characteristic (χ) of 2.
The five Platonic solids have an Euler characteristic of 2. This simply reflects that the surface is a topological 2-sphere, and so is also true, for example, of any polyhedron which is star-shaped with respect to some interior point.
It is one of the Platonic solids, a set of polyhedrons in which the faces are regular polygons that are congruent and the same number of faces meet at a vertex. [2] This set of polyhedrons is named after Plato. In Theaetetus, a dialogue of Plato, Plato hypothesized that the classical elements were made of the five uniform regular solids. Plato ...
The five-fold, three-fold, and two-fold are labeled in blue, red, and magenta respectively. The mirror planes are the cyan great circle. The regular icosahedron has six five-fold rotation axes passing through the two opposite vertices, ten three-fold axes rotating a triangular face, and fifteen two-fold axes passing through any of its edges.
The convex regular dodecahedron is one of the five regular Platonic solids and can be represented by its Schläfli symbol {5, 3}. The dual polyhedron is the regular icosahedron {3, 5}, having five equilateral triangles around each vertex.
Editable printable net of an octahedron with interactive 3D view; Paper model of the octahedron; K.J.M. MacLean, A Geometric Analysis of the Five Platonic Solids and Other Semi-Regular Polyhedra; The Uniform Polyhedra; Virtual Reality Polyhedra – The Encyclopedia of Polyhedra Conway Notation for Polyhedra – Try: dP4