Tuesday, November 30, 2010

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Platonic Solids


dihedral angle: it is each of the two parts of space bounded by two half-planes that start from a common edge. It is an ideal geometrical concept, and may represent only part, as two rectangles with a common side, which symbolize two half-planes.


Face: is each of the planes forming a dihedral angle or polyhedron, or each of the polygons forming a polyhedron or limit.


Concave: When at least one of the interior angles of a polygon is greater than 180 °, it is a concave polygon. The inner surface is concave bowl when viewed from above.


Cube or hexahedron regular: a polyhedron of six congruent square faces, one of the so-called Platonic solids.


Dodecahedron: a twelve-sided polyhedron, convex or concave. Their faces are to be polygon of eleven sides or less. If the twelve faces of the dodecahedron are regular pentagons necessarily equal to each other, the dodecahedron is convex and is called regular.


Icosahedron: a twenty-sided polyhedron, convex or concave. Their faces are to be nineteen-sided polygons or less. If the twenty faces are triangles of the icosahedron equilateral necessarily equal to each other, the icosahedron is convex and is called regular, then being a so-called Platonic solids. The conjugate polyhedron of the icosahedron is the dodecahedron.


Octahedron: a polyhedron with eight faces. With this number of faces can be a convex polyhedron or a concave polyhedron. Their faces are to be seven-sided polygons or less.


Tetrahedron: a polyhedron with four faces. With this number of heads is bound to be a convex polyhedron, and triangular faces, three of them were found at each vertex. If the four faces of the tetrahedron are equilateral triangles, necessarily equal to each other, the tetrahedron is called regular.


Polyhedron: is, in the sense given by classical geometry at the end, a solid figure whose faces are flat and contain a finite volume. The word polyhedron comes from the Greek word classic πολύεδρον, poly-many-sided edron.


convex polyhedron: the one in which the segment joining any two points is contained in the polyhedron.


Prism: it is a solid finish by two parallel and equal polygons which are called bases and many sides are parallelograms as the foundation, called faces.

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° · Glossary · °


Platonic Solids .- polyhedra whose faces are all congruent regular polygons is called "polyhedra regular" or "Platonic solids."

Solido .- A three-dimensional object: width, height and depth.
Examples include spheres, cubes, pyramids and cylinders .

Arista .- straight line of intersection of two planes or two surfaces of a polyhedron that intersect: the edge of a polyhedron is the straight line The two sides are cut.






Face .- In geometry, a face is becoming one of the planes forming an angle or polyhedron dihedral , or each of the polygons included or limit a polyhedron .

Vertex (in plane geometry) .-
point at which they are the two rays of an angle or point of intersection of two sides of a figure flat.

Vertex (in geometry) .-
shared Point three or more sides of a solid figure .


Poligono .- A plane shape (two dimensional) with straight sides.

Examples: triangles, rectangles and pentagons.

(Note: A circle is not a polygon because it has a curved side).



Pentagon .- The pentagon is a polygon five equal sides and five equal angles s


.- Regular polygon is having equal angles and equal sides.

Icosahedron .- is a polyhedron that has twenty equilateral triangular faces congruent.



dihedral angle .- is each of the two parts of space bounded by two half-planes starting from a ridge common.


interior angle or inner angle : is an angle formed by two sides a polygon that share a tip common and that is contained within the polygon. A simple polygon has exactly one internal angle for each vertex and is located on the side of the polygon as .


A Dodecahedron .- is a solid which has twelve pentagonal faces identical regular. It is one of the five regular polyhedra.

congruent triangles - Two triangles are congruent only if there is a correspondence such their corresponding parts are congruent.

equilateral triangle .- equilateral triangle three sides and angles equal.


convex polyhedron: is one in which the segment joining any two points is contained in the polyhedron .

Parallelogram: is a special type of quadrilateral (a polygon composed of four sides) whose sides are parallel in pairs .


Cube or hexahedron regular : is a polyhedron of six square faces consistent, being a so-called Platonic solids.


Quadrilateral: is a polygon has four sides. Quadrilaterals can take different forms but they all have four vertices and two diagonal . Other names used to refer to this polygon are tetragon and Quad.

Square .- The square is the geometric figure formed by four straight lines of equal length, called sides, perfectly straight angles at the points of connection between them (corners at 90 degrees).

Polyhedron .- A solid with flat sides ( Greek poly, meaning "many" and "edron that means" faces "). Example: pyramids and prisms.


regular Polyhedra
have all dihedral angles and all angles equal polyhedra and their faces are equal regular polygons.

Tetaedro: A tetrahedron is a polyhedron with four faces. With this number of heads is bound to be a convex polyhedron, and triangular faces, three of them were found at each corner, is a regular triangular pyramid


Tetrahedron
  • 4 faces (equilateral triangles)
  • 4 vertices
  • 6 edges
Cube
  • 6 faces (squares)
  • 8 vertices 12 edges

Octahedron
  • 8 faces (equilateral triangles)
  • 6 vertices 12 edges


Dodecahedron
  • 12 faces (pentagons)
  • 20 vertices 30 edges



icosahedron
  • 20 faces (equilateral triangles)
  • 12 vertices 30 edges