Kepler solid
A Kepler solid isregular nonconvex polyhedron, allfaceswhichregular polygonswhich hassame numberfaces meeting at all its vertices. (comparePlatonic solids). Therefour:
- greater stellated dodecahedron
- lesser stellated dodecahedron
- great dodecahedron
- great icosahedron
The Kepler solids were defined by Johannes Kepler1619, when he noticed thatstellated dodecahedrons (theretwo,greater andlesser) were composed"hidden" dodecadrons (with pentagonal faces) that have faces composedtriangles,thus look like stylized stars. Wentzel Jamnitzer actually foundgreat stellated dodecahedron andgreat dodecahedron in1500s,Paolo Uccello discovereddrewlesser stellated dodecadron in1400s. Kepler's contribution wasrecognizing thatfitdefinitionregular solids, even thoughwere concave rather than convex, astraditional Platonic solids were.
Thereonly four Kepler solids. The other two aregreater icosahedrongreater dodecahedron which were described by Louis Poinsot1809. Some people call thesetwo "Poinsot solids".
A Kepler solid covers its circumscribed sphere more than once, withcentersfaces acting as winding points insolidspentagrammic faces andvertices inothers. Becausethis, theynot necessarily topologically equivalent tosphere as Platonic solids are,in particular V-E+F=2 may not hold.
Trivia: A cutaway view ofgreater dodecahedron was used for1980s puzzle game Alexander's Star.
