the five Platonic solids. In Mysterium Cosmographicum, published in 1596, Kepler proposed a model of the Solar System in which the five solids were set...

In organic chemistry, a Platonic hydrocarbon is a hydrocarbon whose structure matches one of the five Platonic solids, with carbon atoms replacing its...

Archimedean solids. All the Archimedean solids (but not the elongated square gyrobicupola) can be made via Wythoff constructions from the Platonic solids with...

unlike Platonic solids and Archimedean solids, the faces of Catalan solids are not regular polygons. However, the vertex figures of Catalan solids are regular...

Plato's model of existence Platonic idealism Platonic solid, any of the five convex regular polyhedra Platonic crystal, a periodic structure designed to...

with the edges are all equal. It is an example of many type of solids: Platonic solid, regular polyhedron, parallelohedron, zonohedron, and plesiohedron...

specifically metaphysics, the theory of Forms, theory of Ideas, Platonic idealism, or Platonic realism is a theory widely credited to the Classical Greek philosopher...

adding pyramids to the faces of the Platonic solids. This is just a help to visualize the shape of these solids, and not actually a claim that the edge...

pentagonal faces, three meeting at each vertex. It is one of the five Platonic solids. It has 12 faces, 20 vertices, and 30 edges. It is represented by the...

Johnson solids can be constructed by removing the pentagonal pyramids. The regular icosahedron has many relations with other Platonic solids, one of them...

dodecahedra. While the regular dodecahedron shares many features with other Platonic solids, one unique property of it is that one can start at a corner of the...

sketched each of the Platonic solids. In his Mysterium Cosmographicum, Kepler also proposed the Solar System by using the Platonic solids setting into another...

Johnson solids can be constructed from the first few solids (pyramids, cupolae, and a rotunda), together with the Platonic and Archimedean solids, prisms...

meeting at each vertex. There are 5 finite convex regular polyhedra (the Platonic solids), and four regular star polyhedra (the Kepler–Poinsot polyhedra), making...

theoretical philosophy and practical philosophy, and was the founder of the Platonic Academy, a philosophical school in Athens where Plato taught the doctrines...

Platonic solids - regular polyhedra (all faces of the same type) Archimedean solids - polyhedra with more than one polygon face type. Catalan solids -...

highly symmetrical Platonic solids, the Archimedean solids and their duals the Catalan solids, and the regular-faced Johnson solids. Many of the most studied...

vertex-transitivity—they are the Platonic solids and Archimedean solids, as well as prisms and antiprisms. The Johnson solids are named after mathematician...

known is the (convex, non-stellated) regular icosahedron—one of the Platonic solids—whose faces are 20 equilateral triangles. Two kinds of regular icosahedra...

theorems about them, including the classification of the Platonic solids. It was stated for Platonic solids in 1537 in an unpublished manuscript by Francesco...

Geodesic polyhedron Goldberg polyhedron Johnson solid Platonic solid Semiregular polyhedron Archimedean solid Prism Antiprism Kaplan, Craig S.; Hart, George...

as platonics, and does not refer to the teachings of Plato, or the Platonic solids. The term is now in common usage by multiple research groups in Australia...

Platonic solids (tetrahedron, cube, octahedron, dodecahedron, icosahedron). The sixth column supports a teapot. The image is titled "The Six Platonic...

found that each of the five Platonic solids could be uniquely inscribed and circumscribed by spherical orbs; nesting these solids, each encased in a sphere...

as a non-vertex transitive Archimedean solid (a lower class of polyhedra that follow the five Platonic solids). Fourteen possible Bravais lattices exist...

.. (sequence A000944 in the OEIS). The graphs of the Platonic solids have been called Platonic graphs. As well as having all the other properties of...

polyhedra primarily come from the families of platonic solids, Archimedean solids, Catalan solids, and Johnson solids, as well as dihedral symmetry families...

that do not arise from "cut and paste" manipulations of the Platonic and Archimedean solids, although it is a relative of the icosahedron that has fourfold...

that Euclid studied at the Platonic Academy and later taught at the Musaeum; he is regarded as bridging the earlier Platonic tradition in Athens with the...

other Platonic solids, implying that the other solids cannot tile space and that they cannot be dissected into a cube. All of the Archimedean solids have...