In the 10-, 12-, 14-, and 16-faced deltahedra, some vertices have degree 4 and some degree 5. In the 6-faced deltahedron, some vertices have degree 3 and some degree 4. The three regular convex polyhedra are indeed Platonic solids. There are only eight strictly-convex deltahedra: three are regular polyhedra, and five are Johnson solids. The number of faces, edges, and vertices is listed below for each of the eight convex deltahedra. Of these only eight are convex, having 4, 6, 8, 10, 12, 14, 16 and 20 faces. There are infinitely many deltahedra, all having an even number of faces by the handshaking lemma. The name is taken from the Greek upper case delta (Δ), which has the shape of an equilateral triangle. ![]() In geometry, a deltahedron ( plural deltahedra) is a polyhedron whose faces are all equilateral triangles. This figure is not a strictly-convex deltahedron since coplanar faces are not allowed within the definition. This is a truncated tetrahedron with hexagons subdivided into triangles.
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