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  2. Tetrahedron - Wikipedia

    en.wikipedia.org/wiki/Tetrahedron

    self-dual. Net. 3D model of a regular tetrahedron. In geometry, a tetrahedron ( pl.: tetrahedra or tetrahedrons ), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertices. The tetrahedron is the simplest of all the ordinary convex polyhedra.

  3. Vertex (geometry) - Wikipedia

    en.wikipedia.org/wiki/Vertex_(geometry)

    Vertex (geometry) A vertex of an angle is the endpoint where two lines or rays come together. In geometry, a vertex ( pl.: vertices or vertexes) is a point where two or more curves, lines, or edges meet or intersect. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra ...

  4. Congruence (geometry) - Wikipedia

    en.wikipedia.org/wiki/Congruence_(geometry)

    Congruence permits alteration of some properties, such as location and orientation, but leaves others unchanged, like distances and angles. The unchanged properties are called invariants. In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

  5. Ceva's theorem - Wikipedia

    en.wikipedia.org/wiki/Ceva's_theorem

    In Euclidean geometry, Ceva's theorem is a theorem about triangles. Given a triangle ABC, let the lines AO, BO, CO be drawn from the vertices to a common point O (not on one of the sides of ABC ), to meet opposite sides at D, E, F respectively. (The segments AD, BE, CF are known as cevians .) Then, using signed lengths of segments ,

  6. Regular dodecahedron - Wikipedia

    en.wikipedia.org/wiki/Regular_dodecahedron

    The regular dodecahedron is a polyhedron with 12 pentagonal faces, 30 edges, and 20 vertices. [ 1] It is one of the Platonic solids, a set of polyhedrons in which the faces are regular polygons that are congruent and the same number of faces meet at a vertex. [ 2] This set of polyhedrons is named after Plato.

  7. Octant (solid geometry) - Wikipedia

    en.wikipedia.org/wiki/Octant_(solid_geometry)

    Octant (solid geometry) Three axial planes ( x =0, y =0, z =0) divide space into eight octants. The eight (±,±,±) coordinates of the cube vertices are used to denote them. The horizontal plane shows the four quadrants between x - and y -axis. (Vertex numbers are little-endian balanced ternary.) An octant in solid geometry is one of the eight ...

  8. Dodecahedron - Wikipedia

    en.wikipedia.org/wiki/Dodecahedron

    The coordinates of the 12 additional vertices are (0, ±(1 + h), ±(1 − h 2)), (±(1 + h), ±(1 − h 2), 0) and (±(1 − h 2), 0, ±(1 + h)). h is the height of the wedge-shaped "roof" above the faces of that cube with edge length 2. An important case is h = ⁠ 1 / 2 ⁠ (a quarter of the cube edge length) for perfect natural pyrite (also ...

  9. Incenter - Wikipedia

    en.wikipedia.org/wiki/Incenter

    The incircle (whose center is I) touches each side of the triangle. In geometry, the incenterof a triangle is a triangle center, a point defined for any triangle in a way that is independent of the triangle's placement or scale. The incenter may be equivalently defined as the point where the internal angle bisectorsof the triangle cross, as the ...

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