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2 days ago · 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.
3 days ago · The five convex regular polyhedra are known collectively as the Platonic solids. A proof that that there are only five is outlined below. The following table highlights some of the fundamental properties of the five Platonic solids including the face shape and the numbers of vertices, edges, and faces:
4 days ago · The regular tetrahedron is also one of the five regular Platonic solids, a set of polyhedrons in which all of their faces are regular polygons. [4] Known since antiquity, the Platonic solid is named after the Greek philosopher Plato, who associated those four solids with nature.
2 days ago · 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.
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Sep 5, 2024 · polyhedron, In Euclidean geometry, a three-dimensional object composed of a finite number of polygonal surfaces (faces). Technically, a polyhedron is the boundary between the interior and exterior of a solid. In general, polyhedrons are named according to number of faces.
- The Editors of Encyclopaedia Britannica
1 day ago · Group Theory. Objective: To familiarise the 3D geometry of various molecules. To determine the point groups. Introduction: The symmetry relationships in the molecular structure provide the basis for a mathematical theory, called group theory. The mathematics of group theory is predominantly algebra.
Sep 6, 2024 · Euclidean geometry is the study of plane and solid figures on the basis of axioms and theorems employed by the ancient Greek mathematician Euclid. The term refers to the plane and solid geometry commonly taught in secondary school.
