Asimplerobust'strutalgorithm'ispresentedwhich,whengivenagraphembeddedin3Dspace,thickensitsedgesintosolidstruts.Variousapplications,crystallographicandsculptural,areshowninwhichsmoothhigh-genusformsaretheoutput.Atoolboxofalgorithmictechniquesallowforavarietyofnovel,visuallyengagingformsthatexpressamathematicalaesthetic.Insculpturalexamples,hyperbolictessellationsinthePoincaréplanearetransformedinseveralwaystothree-dimensionalnetworksofedgesembodiedwithinaplausiblyorganicorganization.Bytheuseofdifferenttransformationsandadjustableparametersinthealgorithms,avarietyofattractiveformsresult.Thetechniquesproducewatertightboundaryrepresentationsthatcanbebuiltwithsolidfreeformfabricationequipment.Thefinalphysicaloutputsatisfiesthe'coolnesscriterion,'thatpassersbywillpickthemupandsay'Wow,that'scool!'
