Uniform 9-polytope

This inadequacy of the Euler characteristic to reliably distinguish between different topologies in higher dimensions led to the discovery of the more sophisticated Betti numbers.

[1] Similarly, the notion of orientability of a polyhedron is insufficient to characterise the surface twistings of toroidal polytopes, and this led to the use of torsion coefficients.

[1] Uniform 9-polytopes with reflective symmetry can be generated by these three Coxeter groups, represented by permutations of rings of the Coxeter-Dynkin diagrams: Selected regular and uniform 9-polytopes from each family include: The A9 family has symmetry of order 3628800 (10 factorial).

t0{3,3,3,3,3,3,3,3}9-simplex (day) t1{3,3,3,3,3,3,3,3}Rectified 9-simplex (reday) t2{3,3,3,3,3,3,3,3}Birectified 9-simplex (breday) t3{3,3,3,3,3,3,3,3}Trirectified 9-simplex (treday) t4{3,3,3,3,3,3,3,3}Quadrirectified 9-simplex (icoy) t0,1{3,3,3,3,3,3,3,3}Truncated 9-simplex (teday) t0,2{3,3,3,3,3,3,3,3}Cantellated 9-simplex t1,2{3,3,3,3,3,3,3,3}Bitruncated 9-simplex t0,3{3,3,3,3,3,3,3,3}Runcinated 9-simplex t1,3{3,3,3,3,3,3,3,3}Bicantellated 9-simplex t2,3{3,3,3,3,3,3,3,3}Tritruncated 9-simplex (treday) t0,4{3,3,3,3,3,3,3,3}Stericated 9-simplex t1,4{3,3,3,3,3,3,3,3}Biruncinated 9-simplex t2,4{3,3,3,3,3,3,3,3}Tricantellated 9-simplex t3,4{3,3,3,3,3,3,3,3}Quadritruncated 9-simplex t0,5{3,3,3,3,3,3,3,3}Pentellated 9-simplex t1,5{3,3,3,3,3,3,3,3}Bistericated 9-simplex t2,5{3,3,3,3,3,3,3,3}Triruncinated 9-simplex t3,5{3,3,3,3,3,3,3,3}Quadricantellated 9-simplex t0,6{3,3,3,3,3,3,3,3}Hexicated 9-simplex t1,6{3,3,3,3,3,3,3,3}Bipentellated 9-simplex t2,6{3,3,3,3,3,3,3,3}Tristericated 9-simplex t0,7{3,3,3,3,3,3,3,3}Heptellated 9-simplex t1,7{3,3,3,3,3,3,3,3}Bihexicated 9-simplex t0,8{3,3,3,3,3,3,3,3}Octellated 9-simplex t0,1,2{3,3,3,3,3,3,3,3}Cantitruncated 9-simplex t0,1,3{3,3,3,3,3,3,3,3}Runcitruncated 9-simplex t0,2,3{3,3,3,3,3,3,3,3}Runcicantellated 9-simplex t1,2,3{3,3,3,3,3,3,3,3}Bicantitruncated 9-simplex t0,1,4{3,3,3,3,3,3,3,3}Steritruncated 9-simplex t0,2,4{3,3,3,3,3,3,3,3}Stericantellated 9-simplex t1,2,4{3,3,3,3,3,3,3,3}Biruncitruncated 9-simplex t0,3,4{3,3,3,3,3,3,3,3}Steriruncinated 9-simplex t1,3,4{3,3,3,3,3,3,3,3}Biruncicantellated 9-simplex t2,3,4{3,3,3,3,3,3,3,3}Tricantitruncated 9-simplex t0,1,5{3,3,3,3,3,3,3,3}Pentitruncated 9-simplex t0,2,5{3,3,3,3,3,3,3,3}Penticantellated 9-simplex t1,2,5{3,3,3,3,3,3,3,3}Bisteritruncated 9-simplex t0,3,5{3,3,3,3,3,3,3,3}Pentiruncinated 9-simplex t1,3,5{3,3,3,3,3,3,3,3}Bistericantellated 9-simplex t2,3,5{3,3,3,3,3,3,3,3}Triruncitruncated 9-simplex t0,4,5{3,3,3,3,3,3,3,3}Pentistericated 9-simplex t1,4,5{3,3,3,3,3,3,3,3}Bisteriruncinated 9-simplex t2,4,5{3,3,3,3,3,3,3,3}Triruncicantellated 9-simplex t3,4,5{3,3,3,3,3,3,3,3}Quadricantitruncated 9-simplex t0,1,6{3,3,3,3,3,3,3,3}Hexitruncated 9-simplex t0,2,6{3,3,3,3,3,3,3,3}Hexicantellated 9-simplex t1,2,6{3,3,3,3,3,3,3,3}Bipentitruncated 9-simplex t0,3,6{3,3,3,3,3,3,3,3}Hexiruncinated 9-simplex t1,3,6{3,3,3,3,3,3,3,3}Bipenticantellated 9-simplex t2,3,6{3,3,3,3,3,3,3,3}Tristeritruncated 9-simplex t0,4,6{3,3,3,3,3,3,3,3}Hexistericated 9-simplex t1,4,6{3,3,3,3,3,3,3,3}Bipentiruncinated 9-simplex t2,4,6{3,3,3,3,3,3,3,3}Tristericantellated 9-simplex t0,5,6{3,3,3,3,3,3,3,3}Hexipentellated 9-simplex t1,5,6{3,3,3,3,3,3,3,3}Bipentistericated 9-simplex t0,1,7{3,3,3,3,3,3,3,3}Heptitruncated 9-simplex t0,2,7{3,3,3,3,3,3,3,3}Hepticantellated 9-simplex t1,2,7{3,3,3,3,3,3,3,3}Bihexitruncated 9-simplex t0,3,7{3,3,3,3,3,3,3,3}Heptiruncinated 9-simplex t1,3,7{3,3,3,3,3,3,3,3}Bihexicantellated 9-simplex t0,4,7{3,3,3,3,3,3,3,3}Heptistericated 9-simplex t1,4,7{3,3,3,3,3,3,3,3}Bihexiruncinated 9-simplex t0,5,7{3,3,3,3,3,3,3,3}Heptipentellated 9-simplex t0,6,7{3,3,3,3,3,3,3,3}Heptihexicated 9-simplex t0,1,8{3,3,3,3,3,3,3,3}Octitruncated 9-simplex t0,2,8{3,3,3,3,3,3,3,3}Octicantellated 9-simplex t0,3,8{3,3,3,3,3,3,3,3}Octiruncinated 9-simplex t0,4,8{3,3,3,3,3,3,3,3}Octistericated 9-simplex t0,1,2,3{3,3,3,3,3,3,3,3}Runcicantitruncated 9-simplex t0,1,2,4{3,3,3,3,3,3,3,3}Stericantitruncated 9-simplex t0,1,3,4{3,3,3,3,3,3,3,3}Steriruncitruncated 9-simplex t0,2,3,4{3,3,3,3,3,3,3,3}Steriruncicantellated 9-simplex t1,2,3,4{3,3,3,3,3,3,3,3}Biruncicantitruncated 9-simplex t0,1,2,5{3,3,3,3,3,3,3,3}Penticantitruncated 9-simplex t0,1,3,5{3,3,3,3,3,3,3,3}Pentiruncitruncated 9-simplex t0,2,3,5{3,3,3,3,3,3,3,3}Pentiruncicantellated 9-simplex t1,2,3,5{3,3,3,3,3,3,3,3}Bistericantitruncated 9-simplex t0,1,4,5{3,3,3,3,3,3,3,3}Pentisteritruncated 9-simplex t0,2,4,5{3,3,3,3,3,3,3,3}Pentistericantellated 9-simplex t1,2,4,5{3,3,3,3,3,3,3,3}Bisteriruncitruncated 9-simplex t0,3,4,5{3,3,3,3,3,3,3,3}Pentisteriruncinated 9-simplex t1,3,4,5{3,3,3,3,3,3,3,3}Bisteriruncicantellated 9-simplex t2,3,4,5{3,3,3,3,3,3,3,3}Triruncicantitruncated 9-simplex t0,1,2,6{3,3,3,3,3,3,3,3}Hexicantitruncated 9-simplex t0,1,3,6{3,3,3,3,3,3,3,3}Hexiruncitruncated 9-simplex t0,2,3,6{3,3,3,3,3,3,3,3}Hexiruncicantellated 9-simplex t1,2,3,6{3,3,3,3,3,3,3,3}Bipenticantitruncated 9-simplex t0,1,4,6{3,3,3,3,3,3,3,3}Hexisteritruncated 9-simplex t0,2,4,6{3,3,3,3,3,3,3,3}Hexistericantellated 9-simplex t1,2,4,6{3,3,3,3,3,3,3,3}Bipentiruncitruncated 9-simplex t0,3,4,6{3,3,3,3,3,3,3,3}Hexisteriruncinated 9-simplex t1,3,4,6{3,3,3,3,3,3,3,3}Bipentiruncicantellated 9-simplex t2,3,4,6{3,3,3,3,3,3,3,3}Tristericantitruncated 9-simplex t0,1,5,6{3,3,3,3,3,3,3,3}Hexipentitruncated 9-simplex t0,2,5,6{3,3,3,3,3,3,3,3}Hexipenticantellated 9-simplex t1,2,5,6{3,3,3,3,3,3,3,3}Bipentisteritruncated 9-simplex t0,3,5,6{3,3,3,3,3,3,3,3}Hexipentiruncinated 9-simplex t1,3,5,6{3,3,3,3,3,3,3,3}Bipentistericantellated 9-simplex t2,3,5,6{3,3,3,3,3,3,3,3}Tristeriruncitruncated 9-simplex t0,4,5,6{3,3,3,3,3,3,3,3}Hexipentistericated 9-simplex t1,4,5,6{3,3,3,3,3,3,3,3}Bipentisteriruncinated 9-simplex t0,1,2,7{3,3,3,3,3,3,3,3}Hepticantitruncated 9-simplex t0,1,3,7{3,3,3,3,3,3,3,3}Heptiruncitruncated 9-simplex t0,2,3,7{3,3,3,3,3,3,3,3}Heptiruncicantellated 9-simplex t1,2,3,7{3,3,3,3,3,3,3,3}Bihexicantitruncated 9-simplex t0,1,4,7{3,3,3,3,3,3,3,3}Heptisteritruncated 9-simplex t0,2,4,7{3,3,3,3,3,3,3,3}Heptistericantellated 9-simplex t1,2,4,7{3,3,3,3,3,3,3,3}Bihexiruncitruncated 9-simplex t0,3,4,7{3,3,3,3,3,3,3,3}Heptisteriruncinated 9-simplex t1,3,4,7{3,3,3,3,3,3,3,3}Bihexiruncicantellated 9-simplex t0,1,5,7{3,3,3,3,3,3,3,3}Heptipentitruncated 9-simplex t0,2,5,7{3,3,3,3,3,3,3,3}Heptipenticantellated 9-simplex t1,2,5,7{3,3,3,3,3,3,3,3}Bihexisteritruncated 9-simplex t0,3,5,7{3,3,3,3,3,3,3,3}Heptipentiruncinated 9-simplex t1,3,5,7{3,3,3,3,3,3,3,3}Bihexistericantellated 9-simplex t0,4,5,7{3,3,3,3,3,3,3,3}Heptipentistericated 9-simplex t0,1,6,7{3,3,3,3,3,3,3,3}Heptihexitruncated 9-simplex t0,2,6,7{3,3,3,3,3,3,3,3}Heptihexicantellated 9-simplex t1,2,6,7{3,3,3,3,3,3,3,3}Bihexipentitruncated 9-simplex t0,3,6,7{3,3,3,3,3,3,3,3}Heptihexiruncinated 9-simplex t0,4,6,7{3,3,3,3,3,3,3,3}Heptihexistericated 9-simplex t0,5,6,7{3,3,3,3,3,3,3,3}Heptihexipentellated 9-simplex t0,1,2,8{3,3,3,3,3,3,3,3}Octicantitruncated 9-simplex t0,1,3,8{3,3,3,3,3,3,3,3}Octiruncitruncated 9-simplex t0,2,3,8{3,3,3,3,3,3,3,3}Octiruncicantellated 9-simplex t0,1,4,8{3,3,3,3,3,3,3,3}Octisteritruncated 9-simplex t0,2,4,8{3,3,3,3,3,3,3,3}Octistericantellated 9-simplex t0,3,4,8{3,3,3,3,3,3,3,3}Octisteriruncinated 9-simplex t0,1,5,8{3,3,3,3,3,3,3,3}Octipentitruncated 9-simplex t0,2,5,8{3,3,3,3,3,3,3,3}Octipenticantellated 9-simplex t0,3,5,8{3,3,3,3,3,3,3,3}Octipentiruncinated 9-simplex t0,1,6,8{3,3,3,3,3,3,3,3}Octihexitruncated 9-simplex t0,2,6,8{3,3,3,3,3,3,3,3}Octihexicantellated 9-simplex t0,1,7,8{3,3,3,3,3,3,3,3}Octiheptitruncated 9-simplex t0,1,2,3,4{3,3,3,3,3,3,3,3}Steriruncicantitruncated 9-simplex t0,1,2,3,5{3,3,3,3,3,3,3,3}Pentiruncicantitruncated 9-simplex t0,1,2,4,5{3,3,3,3,3,3,3,3}Pentistericantitruncated 9-simplex t0,1,3,4,5{3,3,3,3,3,3,3,3}Pentisteriruncitruncated 9-simplex t0,2,3,4,5{3,3,3,3,3,3,3,3}Pentisteriruncicantellated 9-simplex t1,2,3,4,5{3,3,3,3,3,3,3,3}Bisteriruncicantitruncated 9-simplex t0,1,2,3,6{3,3,3,3,3,3,3,3}Hexiruncicantitruncated 9-simplex t0,1,2,4,6{3,3,3,3,3,3,3,3}Hexistericantitruncated 9-simplex t0,1,3,4,6{3,3,3,3,3,3,3,3}Hexisteriruncitruncated 9-simplex t0,2,3,4,6{3,3,3,3,3,3,3,3}Hexisteriruncicantellated 9-simplex t1,2,3,4,6{3,3,3,3,3,3,3,3}Bipentiruncicantitruncated 9-simplex t0,1,2,5,6{3,3,3,3,3,3,3,3}Hexipenticantitruncated 9-simplex t0,1,3,5,6{3,3,3,3,3,3,3,3}Hexipentiruncitruncated 9-simplex t0,2,3,5,6{3,3,3,3,3,3,3,3}Hexipentiruncicantellated 9-simplex t1,2,3,5,6{3,3,3,3,3,3,3,3}Bipentistericantitruncated 9-simplex t0,1,4,5,6{3,3,3,3,3,3,3,3}Hexipentisteritruncated 9-simplex t0,2,4,5,6{3,3,3,3,3,3,3,3}Hexipentistericantellated 9-simplex t1,2,4,5,6{3,3,3,3,3,3,3,3}Bipentisteriruncitruncated 9-simplex t0,3,4,5,6{3,3,3,3,3,3,3,3}Hexipentisteriruncinated 9-simplex t1,3,4,5,6{3,3,3,3,3,3,3,3}Bipentisteriruncicantellated 9-simplex t2,3,4,5,6{3,3,3,3,3,3,3,3}Tristeriruncicantitruncated 9-simplex t0,1,2,3,7{3,3,3,3,3,3,3,3}Heptiruncicantitruncated 9-simplex t0,1,2,4,7{3,3,3,3,3,3,3,3}Heptistericantitruncated 9-simplex t0,1,3,4,7{3,3,3,3,3,3,3,3}Heptisteriruncitruncated 9-simplex t0,2,3,4,7{3,3,3,3,3,3,3,3}Heptisteriruncicantellated 9-simplex t1,2,3,4,7{3,3,3,3,3,3,3,3}Bihexiruncicantitruncated 9-simplex t0,1,2,5,7{3,3,3,3,3,3,3,3}Heptipenticantitruncated 9-simplex t0,1,3,5,7{3,3,3,3,3,3,3,3}Heptipentiruncitruncated 9-simplex t0,2,3,5,7{3,3,3,3,3,3,3,3}Heptipentiruncicantellated 9-simplex t1,2,3,5,7{3,3,3,3,3,3,3,3}Bihexistericantitruncated 9-simplex t0,1,4,5,7{3,3,3,3,3,3,3,3}Heptipentisteritruncated 9-simplex t0,2,4,5,7{3,3,3,3,3,3,3,3}Heptipentistericantellated 9-simplex t1,2,4,5,7{3,3,3,3,3,3,3,3}Bihexisteriruncitruncated 9-simplex t0,3,4,5,7{3,3,3,3,3,3,3,3}Heptipentisteriruncinated 9-simplex t1,3,4,5,7{3,3,3,3,3,3,3,3}Bihexisteriruncicantellated 9-simplex t0,1,2,6,7{3,3,3,3,3,3,3,3}Heptihexicantitruncated 9-simplex t0,1,3,6,7{3,3,3,3,3,3,3,3}Heptihexiruncitruncated 9-simplex t0,2,3,6,7{3,3,3,3,3,3,3,3}Heptihexiruncicantellated 9-simplex t1,2,3,6,7{3,3,3,3,3,3,3,3}Bihexipenticantitruncated 9-simplex t0,1,4,6,7{3,3,3,3,3,3,3,3}Heptihexisteritruncated 9-simplex t0,2,4,6,7{3,3,3,3,3,3,3,3}Heptihexistericantellated 9-simplex t1,2,4,6,7{3,3,3,3,3,3,3,3}Bihexipentiruncitruncated 9-simplex t0,3,4,6,7{3,3,3,3,3,3,3,3}Heptihexisteriruncinated 9-simplex t0,1,5,6,7{3,3,3,3,3,3,3,3}Heptihexipentitruncated 9-simplex t0,2,5,6,7{3,3,3,3,3,3,3,3}Heptihexipenticantellated 9-simplex t0,3,5,6,7{3,3,3,3,3,3,3,3}Heptihexipentiruncinated 9-simplex t0,4,5,6,7{3,3,3,3,3,3,3,3}Heptihexipentistericated 9-simplex t0,1,2,3,8{3,3,3,3,3,3,3,3}Octiruncicantitruncated 9-simplex t0,1,2,4,8{3,3,3,3,3,3,3,3}Octistericantitruncated 9-simplex t0,1,3,4,8{3,3,3,3,3,3,3,3}Octisteriruncitruncated 9-simplex t0,2,3,4,8{3,3,3,3,3,3,3,3}Octisteriruncicantellated 9-simplex t0,1,2,5,8{3,3,3,3,3,3,3,3}Octipenticantitruncated 9-simplex t0,1,3,5,8{3,3,3,3,3,3,3,3}Octipentiruncitruncated 9-simplex t0,2,3,5,8{3,3,3,3,3,3,3,3}Octipentiruncicantellated 9-simplex t0,1,4,5,8{3,3,3,3,3,3,3,3}Octipentisteritruncated 9-simplex t0,2,4,5,8{3,3,3,3,3,3,3,3}Octipentistericantellated 9-simplex t0,3,4,5,8{3,3,3,3,3,3,3,3}Octipentisteriruncinated 9-simplex t0,1,2,6,8{3,3,3,3,3,3,3,3}Octihexicantitruncated 9-simplex t0,1,3,6,8{3,3,3,3,3,3,3,3}Octihexiruncitruncated 9-simplex t0,2,3,6,8{3,3,3,3,3,3,3,3}Octihexiruncicantellated 9-simplex t0,1,4,6,8{3,3,3,3,3,3,3,3}Octihexisteritruncated 9-simplex t0,2,4,6,8{3,3,3,3,3,3,3,3}Octihexistericantellated 9-simplex t0,1,5,6,8{3,3,3,3,3,3,3,3}Octihexipentitruncated 9-simplex t0,1,2,7,8{3,3,3,3,3,3,3,3}Octihepticantitruncated 9-simplex t0,1,3,7,8{3,3,3,3,3,3,3,3}Octiheptiruncitruncated 9-simplex t0,1,4,7,8{3,3,3,3,3,3,3,3}Octiheptisteritruncated 9-simplex t0,1,2,3,4,5{3,3,3,3,3,3,3,3}Pentisteriruncicantitruncated 9-simplex t0,1,2,3,4,6{3,3,3,3,3,3,3,3}Hexisteriruncicantitruncated 9-simplex t0,1,2,3,5,6{3,3,3,3,3,3,3,3}Hexipentiruncicantitruncated 9-simplex t0,1,2,4,5,6{3,3,3,3,3,3,3,3}Hexipentistericantitruncated 9-simplex t0,1,3,4,5,6{3,3,3,3,3,3,3,3}Hexipentisteriruncitruncated 9-simplex t0,2,3,4,5,6{3,3,3,3,3,3,3,3}Hexipentisteriruncicantellated 9-simplex t1,2,3,4,5,6{3,3,3,3,3,3,3,3}Bipentisteriruncicantitruncated 9-simplex t0,1,2,3,4,7{3,3,3,3,3,3,3,3}Heptisteriruncicantitruncated 9-simplex t0,1,2,3,5,7{3,3,3,3,3,3,3,3}Heptipentiruncicantitruncated 9-simplex t0,1,2,4,5,7{3,3,3,3,3,3,3,3}Heptipentistericantitruncated 9-simplex t0,1,3,4,5,7{3,3,3,3,3,3,3,3}Heptipentisteriruncitruncated 9-simplex t0,2,3,4,5,7{3,3,3,3,3,3,3,3}Heptipentisteriruncicantellated 9-simplex t1,2,3,4,5,7{3,3,3,3,3,3,3,3}Bihexisteriruncicantitruncated 9-simplex t0,1,2,3,6,7{3,3,3,3,3,3,3,3}Heptihexiruncicantitruncated 9-simplex t0,1,2,4,6,7{3,3,3,3,3,3,3,3}Heptihexistericantitruncated 9-simplex t0,1,3,4,6,7{3,3,3,3,3,3,3,3}Heptihexisteriruncitruncated 9-simplex t0,2,3,4,6,7{3,3,3,3,3,3,3,3}Heptihexisteriruncicantellated 9-simplex t1,2,3,4,6,7{3,3,3,3,3,3,3,3}Bihexipentiruncicantitruncated 9-simplex t0,1,2,5,6,7{3,3,3,3,3,3,3,3}Heptihexipenticantitruncated 9-simplex t0,1,3,5,6,7{3,3,3,3,3,3,3,3}Heptihexipentiruncitruncated 9-simplex t0,2,3,5,6,7{3,3,3,3,3,3,3,3}Heptihexipentiruncicantellated 9-simplex t1,2,3,5,6,7{3,3,3,3,3,3,3,3}Bihexipentistericantitruncated 9-simplex t0,1,4,5,6,7{3,3,3,3,3,3,3,3}Heptihexipentisteritruncated 9-simplex t0,2,4,5,6,7{3,3,3,3,3,3,3,3}Heptihexipentistericantellated 9-simplex t0,3,4,5,6,7{3,3,3,3,3,3,3,3}Heptihexipentisteriruncinated 9-simplex t0,1,2,3,4,8{3,3,3,3,3,3,3,3}Octisteriruncicantitruncated 9-simplex t0,1,2,3,5,8{3,3,3,3,3,3,3,3}Octipentiruncicantitruncated 9-simplex t0,1,2,4,5,8{3,3,3,3,3,3,3,3}Octipentistericantitruncated 9-simplex t0,1,3,4,5,8{3,3,3,3,3,3,3,3}Octipentisteriruncitruncated 9-simplex t0,2,3,4,5,8{3,3,3,3,3,3,3,3}Octipentisteriruncicantellated 9-simplex t0,1,2,3,6,8{3,3,3,3,3,3,3,3}Octihexiruncicantitruncated 9-simplex t0,1,2,4,6,8{3,3,3,3,3,3,3,3}Octihexistericantitruncated 9-simplex t0,1,3,4,6,8{3,3,3,3,3,3,3,3}Octihexisteriruncitruncated 9-simplex t0,2,3,4,6,8{3,3,3,3,3,3,3,3}Octihexisteriruncicantellated 9-simplex t0,1,2,5,6,8{3,3,3,3,3,3,3,3}Octihexipenticantitruncated 9-simplex t0,1,3,5,6,8{3,3,3,3,3,3,3,3}Octihexipentiruncitruncated 9-simplex t0,2,3,5,6,8{3,3,3,3,3,3,3,3}Octihexipentiruncicantellated 9-simplex t0,1,4,5,6,8{3,3,3,3,3,3,3,3}Octihexipentisteritruncated 9-simplex t0,1,2,3,7,8{3,3,3,3,3,3,3,3}Octiheptiruncicantitruncated 9-simplex t0,1,2,4,7,8{3,3,3,3,3,3,3,3}Octiheptistericantitruncated 9-simplex t0,1,3,4,7,8{3,3,3,3,3,3,3,3}Octiheptisteriruncitruncated 9-simplex t0,1,2,5,7,8{3,3,3,3,3,3,3,3}Octiheptipenticantitruncated 9-simplex t0,1,3,5,7,8{3,3,3,3,3,3,3,3}Octiheptipentiruncitruncated 9-simplex t0,1,2,6,7,8{3,3,3,3,3,3,3,3}Octiheptihexicantitruncated 9-simplex t0,1,2,3,4,5,6{3,3,3,3,3,3,3,3}Hexipentisteriruncicantitruncated 9-simplex t0,1,2,3,4,5,7{3,3,3,3,3,3,3,3}Heptipentisteriruncicantitruncated 9-simplex t0,1,2,3,4,6,7{3,3,3,3,3,3,3,3}Heptihexisteriruncicantitruncated 9-simplex t0,1,2,3,5,6,7{3,3,3,3,3,3,3,3}Heptihexipentiruncicantitruncated 9-simplex t0,1,2,4,5,6,7{3,3,3,3,3,3,3,3}Heptihexipentistericantitruncated 9-simplex t0,1,3,4,5,6,7{3,3,3,3,3,3,3,3}Heptihexipentisteriruncitruncated 9-simplex t0,2,3,4,5,6,7{3,3,3,3,3,3,3,3}Heptihexipentisteriruncicantellated 9-simplex t1,2,3,4,5,6,7{3,3,3,3,3,3,3,3}Bihexipentisteriruncicantitruncated 9-simplex t0,1,2,3,4,5,8{3,3,3,3,3,3,3,3}Octipentisteriruncicantitruncated 9-simplex t0,1,2,3,4,6,8{3,3,3,3,3,3,3,3}Octihexisteriruncicantitruncated 9-simplex t0,1,2,3,5,6,8{3,3,3,3,3,3,3,3}Octihexipentiruncicantitruncated 9-simplex t0,1,2,4,5,6,8{3,3,3,3,3,3,3,3}Octihexipentistericantitruncated 9-simplex t0,1,3,4,5,6,8{3,3,3,3,3,3,3,3}Octihexipentisteriruncitruncated 9-simplex t0,2,3,4,5,6,8{3,3,3,3,3,3,3,3}Octihexipentisteriruncicantellated 9-simplex t0,1,2,3,4,7,8{3,3,3,3,3,3,3,3}Octiheptisteriruncicantitruncated 9-simplex t0,1,2,3,5,7,8{3,3,3,3,3,3,3,3}Octiheptipentiruncicantitruncated 9-simplex t0,1,2,4,5,7,8{3,3,3,3,3,3,3,3}Octiheptipentistericantitruncated 9-simplex t0,1,3,4,5,7,8{3,3,3,3,3,3,3,3}Octiheptipentisteriruncitruncated 9-simplex t0,1,2,3,6,7,8{3,3,3,3,3,3,3,3}Octiheptihexiruncicantitruncated 9-simplex t0,1,2,4,6,7,8{3,3,3,3,3,3,3,3}Octiheptihexistericantitruncated 9-simplex t0,1,2,3,4,5,6,7{3,3,3,3,3,3,3,3}Heptihexipentisteriruncicantitruncated 9-simplex t0,1,2,3,4,5,6,8{3,3,3,3,3,3,3,3}Octihexipentisteriruncicantitruncated 9-simplex t0,1,2,3,4,5,7,8{3,3,3,3,3,3,3,3}Octiheptipentisteriruncicantitruncated 9-simplex t0,1,2,3,4,6,7,8{3,3,3,3,3,3,3,3}Octiheptihexisteriruncicantitruncated 9-simplex t0,1,2,3,5,6,7,8{3,3,3,3,3,3,3,3}Octiheptihexipentiruncicantitruncated 9-simplex t0,1,2,3,4,5,6,7,8{3,3,3,3,3,3,3,3}Omnitruncated 9-simplex There are 511 forms based on all permutations of the Coxeter-Dynkin diagrams with one or more rings.

This family has 3×128−1=383 Wythoffian uniform polytopes, generated by marking one or more nodes of the D9 Coxeter-Dynkin diagram.