Overview
- Group
- SmallGroup(1008,903)
- Rank
- 3
- Schläfli Type
- {21,12}
- Vertices, edges, …
- 42, 252, 24
- 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 := ( 3, 4)( 5,25)( 6,26)( 7,28)( 8,27)( 9,21)(10,22)(11,24)(12,23)(13,17)(14,18)(15,20)(16,19)(29,57)(30,58)(31,60)(32,59)(33,81)(34,82)(35,84)(36,83)(37,77)(38,78)(39,80)(40,79)(41,73)(42,74)(43,76)(44,75)(45,69)(46,70)(47,72)(48,71)(49,65)(50,66)(51,68)(52,67)(53,61)(54,62)(55,64)(56,63);; s1 := ( 1,33)( 2,36)( 3,35)( 4,34)( 5,29)( 6,32)( 7,31)( 8,30)( 9,53)(10,56)(11,55)(12,54)(13,49)(14,52)(15,51)(16,50)(17,45)(18,48)(19,47)(20,46)(21,41)(22,44)(23,43)(24,42)(25,37)(26,40)(27,39)(28,38)(57,61)(58,64)(59,63)(60,62)(65,81)(66,84)(67,83)(68,82)(69,77)(70,80)(71,79)(72,78)(74,76);; s2 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,58)(30,57)(31,60)(32,59)(33,62)(34,61)(35,64)(36,63)(37,66)(38,65)(39,68)(40,67)(41,70)(42,69)(43,72)(44,71)(45,74)(46,73)(47,76)(48,75)(49,78)(50,77)(51,80)(52,79)(53,82)(54,81)(55,84)(56,83);; 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*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1,
s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s0,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(84)!( 3, 4)( 5,25)( 6,26)( 7,28)( 8,27)( 9,21)(10,22)(11,24)(12,23)(13,17)(14,18)(15,20)(16,19)(29,57)(30,58)(31,60)(32,59)(33,81)(34,82)(35,84)(36,83)(37,77)(38,78)(39,80)(40,79)(41,73)(42,74)(43,76)(44,75)(45,69)(46,70)(47,72)(48,71)(49,65)(50,66)(51,68)(52,67)(53,61)(54,62)(55,64)(56,63); s1 := Sym(84)!( 1,33)( 2,36)( 3,35)( 4,34)( 5,29)( 6,32)( 7,31)( 8,30)( 9,53)(10,56)(11,55)(12,54)(13,49)(14,52)(15,51)(16,50)(17,45)(18,48)(19,47)(20,46)(21,41)(22,44)(23,43)(24,42)(25,37)(26,40)(27,39)(28,38)(57,61)(58,64)(59,63)(60,62)(65,81)(66,84)(67,83)(68,82)(69,77)(70,80)(71,79)(72,78)(74,76); s2 := Sym(84)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,58)(30,57)(31,60)(32,59)(33,62)(34,61)(35,64)(36,63)(37,66)(38,65)(39,68)(40,67)(41,70)(42,69)(43,72)(44,71)(45,74)(46,73)(47,76)(48,75)(49,78)(50,77)(51,80)(52,79)(53,82)(54,81)(55,84)(56,83); 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*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s0, s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.