Search results
Results from the WOW.Com Content Network
In geometry, a polyhedron (pl.: polyhedra or polyhedrons; from Greek πολύ (poly-) ' many ' and ἕδρον (-hedron) ' base, seat ') is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices. The term "polyhedron" may refer either to a solid figure or to its boundary surface.
One might characterise the Greek definition as follows: A regular polygon is a planar figure with all edges equal and all corners equal. A regular polyhedron is a solid (convex) figure with all faces being congruent regular polygons, the same number arranged all alike around each vertex.
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.
In geometry, a dodecahedron (from Ancient Greek δωδεκάεδρον (dōdekáedron); from δώδεκα (dṓdeka) ' twelve ' and ἕδρα (hédra) ' base, seat, face ') or duodecahedron [1] is any polyhedron with twelve flat faces.
In geometry, an icosahedron (/ ˌ aɪ k ɒ s ə ˈ h iː d r ən,-k ə-,-k oʊ-/ or / aɪ ˌ k ɒ s ə ˈ h iː d r ən / [1]) is a polyhedron with 20 faces. The name comes from Ancient Greek εἴκοσι (eíkosi) ' twenty ' and ἕδρα (hédra) ' seat '. The plural can be either "icosahedra" (/-d r ə /) or "icosahedrons".
The context of his definition was vague until Heron of Alexandria defined it as the figure by putting the point together with a polygonal base. [9] A prismatoid is defined as a polyhedron where its vertices lie on two parallel planes, with its lateral faces as triangles, trapezoids, and parallelograms. [10] Pyramids are classified as prismatoid ...
This equation, stated by Euler in 1758, [3] is known as Euler's polyhedron formula. [4] It corresponds to the Euler characteristic of the sphere (i.e. χ = 2 {\displaystyle \ \chi =2\ } ), and applies identically to spherical polyhedra .
A deltahedron is a polyhedron whose faces are all equilateral triangles. The deltahedron was named by Martyn Cundy, after the Greek capital letter delta resembling a triangular shape Δ. [1] Deltahedra can be categorized by the property of convexity. The simplest convex deltahedron is the regular tetrahedron, a pyramid with four equilateral ...