Overview
- Group
- SmallGroup(1008,904)
- Rank
- 3
- Schläfli Type
- {6,21}
- Vertices, edges, …
- 24, 252, 84
- Order of s0s1s2
- 84
- Order of s0s1s2s1
- 6
- 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
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.
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s2*s1> of order 2
42 facets
- 42 of {6}*12
12 vertex figures
- 12 of {21}*42
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 7, 8)(11,12)(15,16)(19,20)(23,24)(27,28)(31,32)(35,36)(39,40)(43,44)(47,48)(51,52)(55,56)(59,60)(63,64)(67,68)(71,72)(75,76)(79,80)(83,84);; s1 := ( 2, 4)( 5,25)( 6,28)( 7,27)( 8,26)( 9,21)(10,24)(11,23)(12,22)(13,17)(14,20)(15,19)(16,18)(29,57)(30,60)(31,59)(32,58)(33,81)(34,84)(35,83)(36,82)(37,77)(38,80)(39,79)(40,78)(41,73)(42,76)(43,75)(44,74)(45,69)(46,72)(47,71)(48,70)(49,65)(50,68)(51,67)(52,66)(53,61)(54,64)(55,63)(56,62);; s2 := ( 1,34)( 2,33)( 3,35)( 4,36)( 5,30)( 6,29)( 7,31)( 8,32)( 9,54)(10,53)(11,55)(12,56)(13,50)(14,49)(15,51)(16,52)(17,46)(18,45)(19,47)(20,48)(21,42)(22,41)(23,43)(24,44)(25,38)(26,37)(27,39)(28,40)(57,62)(58,61)(59,63)(60,64)(65,82)(66,81)(67,83)(68,84)(69,78)(70,77)(71,79)(72,80)(73,74);; 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*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1,
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)!( 3, 4)( 7, 8)(11,12)(15,16)(19,20)(23,24)(27,28)(31,32)(35,36)(39,40)(43,44)(47,48)(51,52)(55,56)(59,60)(63,64)(67,68)(71,72)(75,76)(79,80)(83,84); s1 := Sym(84)!( 2, 4)( 5,25)( 6,28)( 7,27)( 8,26)( 9,21)(10,24)(11,23)(12,22)(13,17)(14,20)(15,19)(16,18)(29,57)(30,60)(31,59)(32,58)(33,81)(34,84)(35,83)(36,82)(37,77)(38,80)(39,79)(40,78)(41,73)(42,76)(43,75)(44,74)(45,69)(46,72)(47,71)(48,70)(49,65)(50,68)(51,67)(52,66)(53,61)(54,64)(55,63)(56,62); s2 := Sym(84)!( 1,34)( 2,33)( 3,35)( 4,36)( 5,30)( 6,29)( 7,31)( 8,32)( 9,54)(10,53)(11,55)(12,56)(13,50)(14,49)(15,51)(16,52)(17,46)(18,45)(19,47)(20,48)(21,42)(22,41)(23,43)(24,44)(25,38)(26,37)(27,39)(28,40)(57,62)(58,61)(59,63)(60,64)(65,82)(66,81)(67,83)(68,84)(69,78)(70,77)(71,79)(72,80)(73,74); 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*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, 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.