In 3D space, with n distinct points, what is the maximal number of unit distance lengths? I'm trying to build up a sequence for OEIS, but I'm only positive I've got the right values on two or three of the entries. Here's what I have so far. V -- E -- figure 4 -- 6 -- tetrahedron 5 -- 9 -- triangular bipyramid 6 -- 12 -- octahedron 7 -- 15 -- pentagonal bipyramid 8 -- 18 -- snub disphenoid or Raiskii spindle 9 -- 21 -- triaugmented triangular prism 10 -- 25 -- Nechustan spindle 11 -- 28 -- Augmented Nechustan spindle 12 -- 31 -- Double Pacman spindle 13 -- 36 -- Cuboctahedron + center 14 -- 40 -- Cuboctahedron + center + pyramid 15 -- 45 -- Icosahedron + 3 internal points 16 -- 50 -- Icosahedron + 4 internal points http://math.stackexchange.com/questions/1830194/maximal-unit-lengths-in-3d-w... has a bit more info. Ed Pegg Jr