Overview
- Group
- SmallGroup(1728,47874)
- Rank
- 6
- Schläfli Type
- {6,4,3,2,3}
- Vertices, edges, …
- 6, 24, 12, 6, 3, 3
- Order of s0s1s2s3s4s5
- 6
- Order of s0s1s2s3s4s5s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
4-fold
6-fold
8-fold
12-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 5, 9)( 6,10)( 7,11)( 8,12)(17,21)(18,22)(19,23)(20,24)(29,33)(30,34)(31,35)(32,36)(41,45)(42,46)(43,47)(44,48)(53,57)(54,58)(55,59)(56,60)(65,69)(66,70)(67,71)(68,72);; s1 := ( 1,42)( 2,41)( 3,44)( 4,43)( 5,38)( 6,37)( 7,40)( 8,39)( 9,46)(10,45)(11,48)(12,47)(13,54)(14,53)(15,56)(16,55)(17,50)(18,49)(19,52)(20,51)(21,58)(22,57)(23,60)(24,59)(25,66)(26,65)(27,68)(28,67)(29,62)(30,61)(31,64)(32,63)(33,70)(34,69)(35,72)(36,71);; s2 := ( 2, 3)( 6, 7)(10,11)(13,25)(14,27)(15,26)(16,28)(17,29)(18,31)(19,30)(20,32)(21,33)(22,35)(23,34)(24,36)(38,39)(42,43)(46,47)(49,61)(50,63)(51,62)(52,64)(53,65)(54,67)(55,66)(56,68)(57,69)(58,71)(59,70)(60,72);; s3 := ( 1,13)( 2,14)( 3,16)( 4,15)( 5,17)( 6,18)( 7,20)( 8,19)( 9,21)(10,22)(11,24)(12,23)(27,28)(31,32)(35,36)(37,49)(38,50)(39,52)(40,51)(41,53)(42,54)(43,56)(44,55)(45,57)(46,58)(47,60)(48,59)(63,64)(67,68)(71,72);; s4 := (74,75);; s5 := (73,74);; poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s0*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s2*s3*s2*s3*s2*s3,
s4*s5*s4*s5*s4*s5, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(75)!( 5, 9)( 6,10)( 7,11)( 8,12)(17,21)(18,22)(19,23)(20,24)(29,33)(30,34)(31,35)(32,36)(41,45)(42,46)(43,47)(44,48)(53,57)(54,58)(55,59)(56,60)(65,69)(66,70)(67,71)(68,72); s1 := Sym(75)!( 1,42)( 2,41)( 3,44)( 4,43)( 5,38)( 6,37)( 7,40)( 8,39)( 9,46)(10,45)(11,48)(12,47)(13,54)(14,53)(15,56)(16,55)(17,50)(18,49)(19,52)(20,51)(21,58)(22,57)(23,60)(24,59)(25,66)(26,65)(27,68)(28,67)(29,62)(30,61)(31,64)(32,63)(33,70)(34,69)(35,72)(36,71); s2 := Sym(75)!( 2, 3)( 6, 7)(10,11)(13,25)(14,27)(15,26)(16,28)(17,29)(18,31)(19,30)(20,32)(21,33)(22,35)(23,34)(24,36)(38,39)(42,43)(46,47)(49,61)(50,63)(51,62)(52,64)(53,65)(54,67)(55,66)(56,68)(57,69)(58,71)(59,70)(60,72); s3 := Sym(75)!( 1,13)( 2,14)( 3,16)( 4,15)( 5,17)( 6,18)( 7,20)( 8,19)( 9,21)(10,22)(11,24)(12,23)(27,28)(31,32)(35,36)(37,49)(38,50)(39,52)(40,51)(41,53)(42,54)(43,56)(44,55)(45,57)(46,58)(47,60)(48,59)(63,64)(67,68)(71,72); s4 := Sym(75)!(74,75); s5 := Sym(75)!(73,74); poly := sub<Sym(75)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, s2*s3*s2*s3*s2*s3, s4*s5*s4*s5*s4*s5, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;