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...

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

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

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

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

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 an example of Platonic solids, described as cosmic stellation by Plato in his dialogues, and it was...

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...

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

published a list including ninety-two Johnson solids—excluding the five Platonic solids, the thirteen Archimedean solids, the infinitely many uniform prisms, and...

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

\mathrm {O} _{\mathrm {h} }} . The regular octahedron is one of the Platonic solids, a set of polyhedrons whose faces are congruent regular polygons and...

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

they are isogonal; examples include Platonic and Archimedean solids as well as prisms and antiprisms. The Johnson solids are named after American mathematician...

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

include the family of prismatoid, the Platonic solids, the Archimedean solids and their duals the Catalan solids, and the regular polygonal faces polyhedron...

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 It was stated for Platonic solids in 1537 in an unpublished manuscript by Francesco...

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

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...

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...

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

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

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

.. (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...

prisms and antiprisms, the convex polyhedrons as in 5 Platonic solids and 13 Archimedean solids—2 quasiregular and 11 semiregular— the non-convex star...

attention given to the Platonic solid arrangements over less symmetrical arrangements of knobs over the balls, and some of the five solids do not appear. List...

polyhedra. Because of this, three-dimensional n-flakes are also called platonic solid fractals. In three dimensions, the fractals' volume is zero. A Sierpinski...

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...