Answer the following question: Information: - 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 formula_1. - In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells. It is also known as a C, pentachoron, pentatope, pentahedroid, or tetrahedral pyramid. It is a 4-simplex, the simplest possible convex regular 4-polytope (four-dimensional analogue of a Platonic solid), and is analogous to the tetrahedron in three dimensions and the triangle in two dimensions. The pentachoron is a four dimensional pyramid with a tetrahedral base. - In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons) is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ordinary convex polyhedra and the only one that has fewer than 5 faces. - In elementary geometry, a polytope is a geometric object with flat sides, and may exist in any general number of dimensions "n" as an "n"-dimensional polytope or "n"-polytope. For example, a two-dimensional polygon is a 2-polytope and a three-dimensional polyhedron is a 3-polytope. - In geometry, a 4-polytope (sometimes also called a polychoron, polycell, or polyhedroid) is a four-dimensional polytope. It is a connected and closed figure, composed of lower-dimensional polytopal elements: vertices, edges, faces (polygons), and cells (polyhedra). Each face is shared by exactly two cells. - In five - dimensional geometry , a 5 - simplex is a self - dual regular 5 - polytope . It has 6 vertices , 15 edges , 20 triangle faces , 15 tetrahedral cells , and 6 5 - cell facets . It has a dihedral angle of cos 1 ( 1/5 ) , or approximately 78.46 . - In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. Specifically, a "k"-simplex is a "k"-dimensional polytope which is the convex hull of its "k"+1 vertices. More formally, suppose the "k"+1 points formula_1 are affinely independent, which means formula_2 are linearly independent. Then, the simplex determined by them is the set of points - In three-dimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent regular polygonal faces with the same number of faces meeting at each vertex. Five solids meet those criteria: - In five-dimensional geometry, a five-dimensional polytope or 5-polytope is a 5-dimensional polytope, bounded by (4-polytope) facets. Each polyhedral cell being shared by exactly two 4-polytope facets. Given the paragraphs above, decide what entity has the relation 'has facet polytope' with 'pentachoron'.
Answer:
5-simplex