# Thomson cubic

Last updated The Thomson cubic (black curve) contains the point X whose isogonal conjugate (X') is on the line X(2)-X.

In geometry, the Thomson cubic of a triangle is the locus of centers of circumconics whose normals at the vertices are concurrent. Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted . In geometry, a locus is a set of all points, whose location satisfies or is determined by one or more specified conditions.

## Related Research Articles In geometry, a cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces. A cuboctahedron has 12 identical vertices, with 2 triangles and 2 squares meeting at each, and 24 identical edges, each separating a triangle from a square. As such, it is a quasiregular polyhedron, i.e. an Archimedean solid that is not only vertex-transitive but also edge-transitive. In geometry, the rhombicuboctahedron, or small rhombicuboctahedron, is an Archimedean solid with eight triangular and eighteen square faces. There are 24 identical vertices, with one triangle and three squares meeting at each. The polyhedron has octahedral symmetry, like the cube and octahedron. Its dual is called the deltoidal icositetrahedron or trapezoidal icositetrahedron, although its faces are not really true trapezoids. In geometry, the truncated cube, or truncated hexahedron, is an Archimedean solid. It has 14 regular faces, 36 edges, and 24 vertices. In geometry, a heptagon is a seven-sided polygon or 7-gon.

In algebraic geometry and computational geometry, general position is a notion of genericity for a set of points, or other geometric objects. It means the general case situation, as opposed to some more special or coincidental cases that are possible, which is referred to as special position. Its precise meaning differs in different settings. In mathematics, a cubic plane curve is a plane algebraic curve C defined by a cubic equation In projective geometry, Pascal's theorem states that if six arbitrary points are chosen on a conic and joined by line segments in any order to form a hexagon, then the three pairs of opposite sides of the hexagon meet at three points which lie on a straight line, called the Pascal line of the hexagon. It is named after Blaise Pascal. In geometry, a triakis tetrahedron is a Catalan solid with 12 faces. Each Catalan solid is the dual of an Archimedean solid. The dual of the triakis tetrahedron is the truncated tetrahedron. In geometry, a tetrakis hexahedron is a Catalan solid. Its dual is the truncated octahedron, an Archimedean solid. In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.

Thomson may refer to: In geometry, the Pappus configuration is a configuration of nine points and nine lines in the Euclidean plane, with three points per line and three lines through each point. In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides. A right triangular prism has rectangular sides, otherwise it is oblique. A uniform triangular prism is a right triangular prism with equilateral bases, and square sides. In geometry, the truncated square tiling is a semiregular tiling by regular polygons of the Euclidean plane with one square and two octagons on each vertex. This is the only edge-to-edge tiling by regular convex polygons which contains an octagon. It has Schläfli symbol of t{4,4}. In geometry, the trihexagonal tiling is one of 11 uniform tilings of the Euclidean plane by regular polygons. It consists of equilateral triangles and regular hexagons, arranged so that each hexagon is surrounded by triangles and vice versa. The name derives from the fact that it combines a regular hexagonal tiling and a regular triangular tiling. Two hexagons and two triangles alternate around each vertex, and its edges form an infinite arrangement of lines. Its dual is the rhombille tiling. The cubic honeycomb or cubic cellulation is the only regular space-filling tessellation in Euclidean 3-space, made up of cubic cells. It has 4 cubes around every edge, and 8 cubes around each vertex. Its vertex figure is a regular octahedron. It is a self-dual tessellation with Schläfli symbol {4,3,4}. John Horton Conway calls this honeycomb a cubille. The quarter cubic honeycomb, quarter cubic cellulation or bitruncated alternated cubic honeycomb is a space-filling tessellation in Euclidean 3-space. It is composed of tetrahedra and truncated tetrahedra in a ratio of 1:1. It is called "quarter-cubic" because its symmetry unit – the minimal block from which the pattern is developed by reflections – consists of four such units of the cubic honeycomb. The tetragonal disphenoid tetrahedral honeycomb is a space-filling tessellation in Euclidean 3-space made up of identical tetragonal disphenoidal cells. Cells are face-transitive with 4 identical isosceles triangle faces. John Horton Conway calls it an oblate tetrahedrille or shortened to obtetrahedrille.