final geometry complete final complete final includes cells seventeenth given model index figure interpretations described irregular star self intersecting identical self intersecting faces edges simple triangular faces edges interpretation useful model building researched create regular star complete irregular faces studied history applied process recognizing small great regular rediscovered great great regular star called star proving regular star extended theory regular forms identified including complete published list forms including reflective copies including complete book stated set rules regular gave systematic conform rules complete referenced eighth book book final included 17th model index number named database small covered coarse hair spines ball protect interpretations extends faces infinite planes generates new bounded planes faces intersections planes edges regular according set rules forward including complete symbol complete includes cells including layer simple simple visible surface outward form final composed triangular faces triangular regions join edges turn meet characteristic lie surfaces concentric spheres group form regular layer form regular outer layer form truncated spheres ratio formula regarded dimensional solid object edge lengths golden ratio complete surface area formula volume formula star complete seen self intersecting star having faces corresponding faces underlying face irregular star faces meet layer visible form tips spines edges edge star includes connects visible edges regarded star complete noble face
Final stellation of the icosahedron