Overview
- Group
- SmallGroup(1152,157863)
- Rank
- 5
- Schläfli Type
- {6,6,2,2}
- Vertices, edges, …
- 24, 72, 24, 2, 2
- Order of s0s1s2s3s4
- 12
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
8-fold
12-fold
24-fold
36-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 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);; s1 := ( 1,13)( 2,14)( 3,16)( 4,15)( 5,21)( 6,22)( 7,24)( 8,23)( 9,17)(10,18)(11,20)(12,19)(27,28)(29,33)(30,34)(31,36)(32,35)(37,49)(38,50)(39,52)(40,51)(41,57)(42,58)(43,60)(44,59)(45,53)(46,54)(47,56)(48,55)(63,64)(65,69)(66,70)(67,72)(68,71);; s2 := ( 1,44)( 2,42)( 3,43)( 4,41)( 5,40)( 6,38)( 7,39)( 8,37)( 9,48)(10,46)(11,47)(12,45)(13,68)(14,66)(15,67)(16,65)(17,64)(18,62)(19,63)(20,61)(21,72)(22,70)(23,71)(24,69)(25,56)(26,54)(27,55)(28,53)(29,52)(30,50)(31,51)(32,49)(33,60)(34,58)(35,59)(36,57);; s3 := (73,74);; s4 := (75,76);; poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(76)!( 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); s1 := Sym(76)!( 1,13)( 2,14)( 3,16)( 4,15)( 5,21)( 6,22)( 7,24)( 8,23)( 9,17)(10,18)(11,20)(12,19)(27,28)(29,33)(30,34)(31,36)(32,35)(37,49)(38,50)(39,52)(40,51)(41,57)(42,58)(43,60)(44,59)(45,53)(46,54)(47,56)(48,55)(63,64)(65,69)(66,70)(67,72)(68,71); s2 := Sym(76)!( 1,44)( 2,42)( 3,43)( 4,41)( 5,40)( 6,38)( 7,39)( 8,37)( 9,48)(10,46)(11,47)(12,45)(13,68)(14,66)(15,67)(16,65)(17,64)(18,62)(19,63)(20,61)(21,72)(22,70)(23,71)(24,69)(25,56)(26,54)(27,55)(28,53)(29,52)(30,50)(31,51)(32,49)(33,60)(34,58)(35,59)(36,57); s3 := Sym(76)!(73,74); s4 := Sym(76)!(75,76); poly := sub<Sym(76)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1 >;