has_facet_polytope triaugmented triangular prism
In Euclidean geometry , a regular ___MASK46___ is a ___MASK46___ 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 . 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 ___MASK43___ of which is a regular polygon . There is no requirement that each ___MASK43___ must be the same polygon , or that the same polygons join around each ___MASK49___ . An example of a Johnson solid is the square - based pyramid with equilateral sides (" J "); it has 1 square ___MASK43___ and 4 triangular faces . 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 ___MASK58___ 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 . In geometry , an ___MASK79___ 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 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 ___MASK49___ . Five solids meet those criteria : 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 ___MASK79___ . 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 ___MASK46___ ) and excluding the prisms and antiprisms . They differ from the Johnson solids , whose regular polygonal faces do not meet in identical vertices . In geometry , an " n "- sided antiprism is a polyhedron composed of two parallel copies of some particular " n "- sided ___MASK46___ , connected by an alternating band of triangles . Antiprisms are a subclass of the prismatoids and are a ( degenerate ) type of snub polyhedra .