query: has_facet_polytope triaugmented triangular prism
supports: In geometry , the triaugmented triangular prism or tetracaidecadeltahedron is one of the Johnson solids ( J51 ) . As the name suggests , it can be constructed by attaching square pyramids ( J1 ) to each of the three equatorial faces of the triangular prism . It is a deltahedron . A Johnson solid is one of 92 strictly convex polyhedra that have regular faces but are not uniform ( that is , they are not Platonic solids , Archimedean solids , prisms or antiprisms ) . They were named by Norman Johnson , who first listed these polyhedra in 1966 . A deltahedron (plural "deltahedra") is a polyhedron whose faces are all equilateral triangles. The name is taken from the Greek majuscule delta (formula_1), which has the shape of an equilateral triangle. There are infinitely many deltahedra, but of these only eight are convex, having 4, 6, 8, 10, 12, 14, 16 and 20 faces. The number of faces, edges, and vertices is listed below for each of the eight convex deltahedra. In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes. They are the semi-regular convex polyhedrons composed of regular polygons meeting in identical vertices, excluding the 5 Platonic solids (which are composed of only one type of polygon) and excluding the prisms and antiprisms. They differ from the Johnson solids, whose regular polygonal faces do not meet in identical vertices. 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 geometry, an equilateral triangle is a triangle in which all three sides are equal. In the familiar Euclidean geometry, equilateral triangles are also equiangular; that is, all three internal angles are also congruent to each other and are each 60°. They are regular polygons, and can therefore also be referred to as regular triangles. In geometry, an "n"-sided antiprism is a polyhedron composed of two parallel copies of some particular "n"-sided polygon, connected by an alternating band of triangles. Antiprisms are a subclass of the prismatoids and are a (degenerate) type of snub polyhedra.  In geometry, a Johnson solid is a strictly convex polyhedron, which is not uniform (i.e., not a Platonic solid, Archimedean solid, prism or antiprism), and each face of which is a regular polygon. There is no requirement that each face must be the same polygon, or that the same polygons join around each vertex. An example of a Johnson solid is the square-based pyramid with equilateral sides ("J"); it has 1 square face and 4 triangular faces. In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be convex or star. In the limit, a sequence of regular polygons with an increasing number of sides becomes a circle, if the perimeter is fixed, or a regular apeirogon, if the edge length is fixed.
candidates: equilateral triangle face polygon square vertex
answer: equilateral triangle