Regular Polytopes

Polytopesaregeometricalfiguresboundedbyportionsoflines，planes，orhyperplanes.Inplane(twodimensional)geometry，theyareknownaspolygonsandcomprisesuchfiguresastriangles，squares，pentagons，etc.Insolid(threedimensional)geometrytheyareknownaspolyhedraandincludesuchfiguresastetrahedra(atypeofpyramid)，cubes，icosahedra，andmanymore;thepossibilities，infact，areinfinite!H.S.M.Coxeter'sbookistheforemostbookavailableonregularpolyhedra，incorporatingnotonlytheancientGreekworkonthesubject，butalsothevastamountofinformationthathasbeenaccumulatedonthemsince，especiallyinthelasthundredyears.Theauthor，professorofMathematics，UniversityofToronto，hascontributedmuchvaluableworkhimselfonpolytopesandisawell-knownauthorityonthem.
ProfessorCoxeterbeginswiththefundamentalconceptsofplaneandsolidgeometryandthenmovesontomulti-dimensionality.AmongthemanysubjectscoveredareEuler'sformula，rotationgroups，star-polyhedra，truncation，forms，vectors，coordinates，kaleidoscopes，Petriepolygons，sectionsandprojections，andstar-polytopes.Eachchapterendswithahistoricalsummaryshowingwhenandhowtheinformationcontainedthereinwasdiscovered.Numerousfiguresandexamplesandtheauthor'slucidexplanationsalsohelptomakethetextreadilycomprehensible.Althoughthestudyofpolytopesdoeshavesomepracticalapplicationstomineralogy，architecture，linearprogramming，andotherareas，mostpeopleenjoycontemplatingthesefiguressimplybecausetheirsymmetricalshapeshaveanaestheticappeal.Butwhateverthereasons，anyonewithanelementaryknowledgeofgeometryandtrigonometrywillfindthisoneofthebestsourcebooksavailableonthisfascinatingstudy.