Overview
- Group
- SmallGroup(1152,134258)
- Rank
- 5
- Schläfli Type
- {2,4,36,2}
- Vertices, edges, …
- 2, 4, 72, 36, 2
- Order of s0s1s2s3s4
- 36
- 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
9-fold
12-fold
18-fold
24-fold
36-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (39,48)(40,49)(41,50)(42,51)(43,52)(44,53)(45,54)(46,55)(47,56)(57,66)(58,67)(59,68)(60,69)(61,70)(62,71)(63,72)(64,73)(65,74);; s2 := ( 3,39)( 4,41)( 5,40)( 6,46)( 7,45)( 8,47)( 9,43)(10,42)(11,44)(12,48)(13,50)(14,49)(15,55)(16,54)(17,56)(18,52)(19,51)(20,53)(21,57)(22,59)(23,58)(24,64)(25,63)(26,65)(27,61)(28,60)(29,62)(30,66)(31,68)(32,67)(33,73)(34,72)(35,74)(36,70)(37,69)(38,71);; s3 := ( 3, 6)( 4, 8)( 5, 7)( 9,10)(12,15)(13,17)(14,16)(18,19)(21,24)(22,26)(23,25)(27,28)(30,33)(31,35)(32,34)(36,37)(39,60)(40,62)(41,61)(42,57)(43,59)(44,58)(45,64)(46,63)(47,65)(48,69)(49,71)(50,70)(51,66)(52,68)(53,67)(54,73)(55,72)(56,74);; 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*s1*s0*s1,
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, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(76)!(1,2); s1 := Sym(76)!(39,48)(40,49)(41,50)(42,51)(43,52)(44,53)(45,54)(46,55)(47,56)(57,66)(58,67)(59,68)(60,69)(61,70)(62,71)(63,72)(64,73)(65,74); s2 := Sym(76)!( 3,39)( 4,41)( 5,40)( 6,46)( 7,45)( 8,47)( 9,43)(10,42)(11,44)(12,48)(13,50)(14,49)(15,55)(16,54)(17,56)(18,52)(19,51)(20,53)(21,57)(22,59)(23,58)(24,64)(25,63)(26,65)(27,61)(28,60)(29,62)(30,66)(31,68)(32,67)(33,73)(34,72)(35,74)(36,70)(37,69)(38,71); s3 := Sym(76)!( 3, 6)( 4, 8)( 5, 7)( 9,10)(12,15)(13,17)(14,16)(18,19)(21,24)(22,26)(23,25)(27,28)(30,33)(31,35)(32,34)(36,37)(39,60)(40,62)(41,61)(42,57)(43,59)(44,58)(45,64)(46,63)(47,65)(48,69)(49,71)(50,70)(51,66)(52,68)(53,67)(54,73)(55,72)(56,74); 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*s1*s0*s1, 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, s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;