Sol LeWitt famously enumerated all the incomplete open cubes, finding 122 of these connected, non-planar subsets of the edges of the cube. Since then, while several projects have revisited the cube enumeration, no such enumeration has been published for any other interesting solid. In this paper we present work on enumerating all the incomplete open platonic solids, finding 6 tetrahedra, 122 cubes (just like LeWitt), 185 octahedra, 2\,423\,206 dodecahedra and 16\,096\,166 icosahedra.

翻译：索尔·勒维特曾以枚举所有不完全开放立方体而闻名，他发现了立方体棱边构成的122个连通非平面子集。自此之后，尽管多个研究项目重新审视了立方体的枚举问题，但尚未有研究发表对其他有趣多面体的类似枚举结果。本文介绍了枚举所有不完全开放柏拉图多面体的工作，发现了6个四面体、122个立方体（与勒维特的结果一致）、185个八面体、2,423,206个十二面体以及16,096,166个二十面体。