Overview
- Group
- SmallGroup(1008,903)
- Rank
- 3
- Schläfli Type
- {12,21}
- Vertices, edges, …
- 24, 252, 42
- Order of s0s1s2
- 42
- Order of s0s1s2s1
- 12
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
3-fold
4-fold
6-fold
7-fold
12-fold
21-fold
28-fold
36-fold
42-fold
84-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
Representations
Permutation Representation (GAP)
s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)(25,27)(26,28)(29,59)(30,60)(31,57)(32,58)(33,63)(34,64)(35,61)(36,62)(37,67)(38,68)(39,65)(40,66)(41,71)(42,72)(43,69)(44,70)(45,75)(46,76)(47,73)(48,74)(49,79)(50,80)(51,77)(52,78)(53,83)(54,84)(55,81)(56,82);; s1 := ( 1,29)( 2,30)( 3,32)( 4,31)( 5,53)( 6,54)( 7,56)( 8,55)( 9,49)(10,50)(11,52)(12,51)(13,45)(14,46)(15,48)(16,47)(17,41)(18,42)(19,44)(20,43)(21,37)(22,38)(23,40)(24,39)(25,33)(26,34)(27,36)(28,35)(59,60)(61,81)(62,82)(63,84)(64,83)(65,77)(66,78)(67,80)(68,79)(69,73)(70,74)(71,76)(72,75);; s2 := ( 1, 5)( 2, 8)( 3, 7)( 4, 6)( 9,25)(10,28)(11,27)(12,26)(13,21)(14,24)(15,23)(16,22)(18,20)(29,61)(30,64)(31,63)(32,62)(33,57)(34,60)(35,59)(36,58)(37,81)(38,84)(39,83)(40,82)(41,77)(42,80)(43,79)(44,78)(45,73)(46,76)(47,75)(48,74)(49,69)(50,72)(51,71)(52,70)(53,65)(54,68)(55,67)(56,66);; poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1,
s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(84)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)(25,27)(26,28)(29,59)(30,60)(31,57)(32,58)(33,63)(34,64)(35,61)(36,62)(37,67)(38,68)(39,65)(40,66)(41,71)(42,72)(43,69)(44,70)(45,75)(46,76)(47,73)(48,74)(49,79)(50,80)(51,77)(52,78)(53,83)(54,84)(55,81)(56,82); s1 := Sym(84)!( 1,29)( 2,30)( 3,32)( 4,31)( 5,53)( 6,54)( 7,56)( 8,55)( 9,49)(10,50)(11,52)(12,51)(13,45)(14,46)(15,48)(16,47)(17,41)(18,42)(19,44)(20,43)(21,37)(22,38)(23,40)(24,39)(25,33)(26,34)(27,36)(28,35)(59,60)(61,81)(62,82)(63,84)(64,83)(65,77)(66,78)(67,80)(68,79)(69,73)(70,74)(71,76)(72,75); s2 := Sym(84)!( 1, 5)( 2, 8)( 3, 7)( 4, 6)( 9,25)(10,28)(11,27)(12,26)(13,21)(14,24)(15,23)(16,22)(18,20)(29,61)(30,64)(31,63)(32,62)(33,57)(34,60)(35,59)(36,58)(37,81)(38,84)(39,83)(40,82)(41,77)(42,80)(43,79)(44,78)(45,73)(46,76)(47,75)(48,74)(49,69)(50,72)(51,71)(52,70)(53,65)(54,68)(55,67)(56,66); poly := sub<Sym(84)|s0,s1,s2>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1, s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.