| abstract
| - A uniform 5-polytope is a uniform polytope that exists in 5-dimensional Euclidean space. Using a Wythoff construction, the set of uniform 5-polytopes are enumerated below, grouped with the generation symmetry, although there are overlaps as different generators can create the same forms. Regulars and truncations The three regular 5-polytopes above create 2 families of uniform 5-polytopes. Using a naming scheme proposed by Norman Johnson, these are: {3,3,3,3} Family - There are 19 forms.
* {4,3,3,3} - 31 truncated forms 1.
* t_0{4,3,3,3} regular penteract 2.
* t_1{4,3,3,3} rectified penteract 3.
* t_2{4,3,3,3} birectified penteract 4.
* t_3{4,3,3,3} trirectified penteract 5.
* t_4{4,3,3,3} quadrirectified penteract 6.
* t_0,1{4,3,3,3} truncated penteract 7.
* t_1,2{4,3,3,3} bitruncated penteract 8.
* t_2,3{4,3,3,3} tritruncated penteract 9.
* t_3,4{4,3,3,3} quadritruncated penteract 10.
* t_0,2{4,3,3,3} cantellated penteract 11.
* t_1,3{4,3,3,3} bicantellated penteract 12.
* t_2,4{4,3,3,3} tricantellated penteract 13.
* t_0,3{4,3,3,3} runcinated penteract 14.
* t_1,4{4,3,3,3} biruncinated penteract 15.
* t_0,4{4,3,3,3} stericated penteract 16.
* t_0,1,2{4,3,3,3} cantitruncated penteract 17.
* t_1,2,3{4,3,3,3} bicantitruncated penteract 18.
* t_2,3,4{4,3,3,3} tricantitruncated penteract 19.
* t_0,1,3{4,3,3,3} runcitruncated penteract 20.
* t_1,2,4{4,3,3,3} biruncitruncated penteract 21.
* t_0,2,3{4,3,3,3} runcicantellated penteract 22.
* t_1,3,4{4,3,3,3} biruncicantellated penteract 23.
* t_0,1,4{4,3,3,3} steritruncated penteract 24.
* t_0,2,4{4,3,3,3} stericantellated penteract 25.
* t_0,3,4{4,3,3,3} steriruncinated penteract 26.
* t_0,1,2,3{4,3,3,3} runcicantitruncated penteract 27.
* t_1,2,3,4{4,3,3,3} biruncicantitruncated penteract 28.
* t_0,1,2,4{4,3,3,3} stericantitruncated penteract 29.
* t_0,1,3,4{4,3,3,3} steriruncitruncated penteract 30.
* t_0,2,3,4{4,3,3,3} steriruncicantellated penteract 31.
* t_0,1,2,3,4{4,3,3,3} Omnitruncated penteract
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