Overview
- Group
- SmallGroup(1152,152539)
- Rank
- 5
- Schläfli Type
- {2,2,8,18}
- Vertices, edges, …
- 2, 2, 8, 72, 18
- Order of s0s1s2s3s4
- 72
- 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 := (3,4);; s2 := (23,32)(24,33)(25,34)(26,35)(27,36)(28,37)(29,38)(30,39)(31,40)(41,59)(42,60)(43,61)(44,62)(45,63)(46,64)(47,65)(48,66)(49,67)(50,68)(51,69)(52,70)(53,71)(54,72)(55,73)(56,74)(57,75)(58,76);; s3 := ( 5,41)( 6,43)( 7,42)( 8,48)( 9,47)(10,49)(11,45)(12,44)(13,46)(14,50)(15,52)(16,51)(17,57)(18,56)(19,58)(20,54)(21,53)(22,55)(23,68)(24,70)(25,69)(26,75)(27,74)(28,76)(29,72)(30,71)(31,73)(32,59)(33,61)(34,60)(35,66)(36,65)(37,67)(38,63)(39,62)(40,64);; s4 := ( 5, 8)( 6,10)( 7, 9)(11,12)(14,17)(15,19)(16,18)(20,21)(23,26)(24,28)(25,27)(29,30)(32,35)(33,37)(34,36)(38,39)(41,44)(42,46)(43,45)(47,48)(50,53)(51,55)(52,54)(56,57)(59,62)(60,64)(61,63)(65,66)(68,71)(69,73)(70,72)(74,75);; 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, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(76)!(1,2); s1 := Sym(76)!(3,4); s2 := Sym(76)!(23,32)(24,33)(25,34)(26,35)(27,36)(28,37)(29,38)(30,39)(31,40)(41,59)(42,60)(43,61)(44,62)(45,63)(46,64)(47,65)(48,66)(49,67)(50,68)(51,69)(52,70)(53,71)(54,72)(55,73)(56,74)(57,75)(58,76); s3 := Sym(76)!( 5,41)( 6,43)( 7,42)( 8,48)( 9,47)(10,49)(11,45)(12,44)(13,46)(14,50)(15,52)(16,51)(17,57)(18,56)(19,58)(20,54)(21,53)(22,55)(23,68)(24,70)(25,69)(26,75)(27,74)(28,76)(29,72)(30,71)(31,73)(32,59)(33,61)(34,60)(35,66)(36,65)(37,67)(38,63)(39,62)(40,64); s4 := Sym(76)!( 5, 8)( 6,10)( 7, 9)(11,12)(14,17)(15,19)(16,18)(20,21)(23,26)(24,28)(25,27)(29,30)(32,35)(33,37)(34,36)(38,39)(41,44)(42,46)(43,45)(47,48)(50,53)(51,55)(52,54)(56,57)(59,62)(60,64)(61,63)(65,66)(68,71)(69,73)(70,72)(74,75); 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, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;