In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are...

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

they are not necessarily topologically equivalent to the sphere as Platonic solids are, and in particular the Euler relation χ = V − E + F = 2   {\displaystyle...

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

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

intersecting edges. It is an example of many classes of polyhedra: Platonic solid, regular polyhedron, parallelohedron, zonohedron, and plesiohedron....

the regular dodecahedron with regular pentagons as faces, which is a Platonic solid. There are also three regular star dodecahedra, which are constructed...

polyhedron with eight faces. One special case is the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each...

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...

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

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

from the Platonic solids by a process called stellation. Most stellations are not regular. The study of stellations of the Platonic solids was given...

group of each solid were derived from the Platonic solids, resulting from their construction. Some sources say the Archimedean solids are synonymous...

Johnson solid, some authors required that Johnson solids are not uniform. This means that a Johnson solid is not a Platonic solid, Archimedean solid, prism...

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 It was stated for Platonic solids in 1537 in an unpublished manuscript by Francesco...

five regular Platonic solids, a set of polyhedrons in which all of their faces are regular polygons. Known since antiquity, the Platonic solid is named after...

of ρ {\displaystyle \rho } to be the set of nonnegative reals. For any solid object or set of scattered points in n {\displaystyle n} -dimensional Euclidean...

new hexagonal faces. In the chapters below, the chamfers of the five Platonic solids are described in detail. Each is shown in an equilateral version where...

knowledge of the five Platonic solids a millennium before Plato described them. Indeed, some of them exhibit the symmetries of Platonic solids, but the extent...

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

in higher dimensions, including the four-dimensional analogs of the Platonic solids. An arithmetic of four spatial dimensions, called quaternions, was...

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

the largest face any of the five regular three-dimensional regular Platonic solid can have. A conic is determined using five points in the same way that...

authors. Extending the system up to 999 is expressed with these prefixes. Platonic solid Dice List of polygons, polyhedra and polytopes Circle Ellipse Shape...

completely, the most natural packing being the cubic honeycomb. No other Platonic solid can tile space on its own, but some preliminary results are known. Tetrahedra...

itself. Symmetric shapes such as the circle, regular polygons and platonic solids held deep significance for many ancient philosophers and were investigated...

tournament has an odd number of Hamiltonian paths (Rédei 1934) Every platonic solid, considered as a graph, is Hamiltonian The Cayley graph of a finite...

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...

of solids. Book XIII describes the construction of the five regular Platonic solids in a sphere. In the 17th century, three-dimensional space was described...

the five Platonic solids have triangular faces – the tetrahedron, the octahedron, and the icosahedron. Also, three of the five Platonic solids have vertices...