Deltahedra

thumb|A tetrahedron.

thumb|upright=1.6|The eight convex deltahedra. First row: regular tetrahedron, triangular bipyramid, [[regular octahedron, pentagonal bipyramid. Second row: gyroelongated square bipyramid, regular icosahedron, triaugmented triangular prism, snub disphenoid.]] A deltahedron is a polyhedron whose faces are all equilateral triangles. The deltahedron was named by Martyn Cundy, after the Greek capital letter delta resembling a triangular shape Δ.

Platonic solid

Platonic solid

bipyramid over a triangle

third of the infinite set of face-transitive bipyramids

Catalan polyhedron

Kepler–Poinsot polyhedron

Platonic solid

Johnson solid

solid that has only equilateral triangles as faces

Johnson solid