Polytope of Type {22,22}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,22}*968c
if this polytope has a name.
Group : SmallGroup(968,39)
Rank : 3
Schlafli Type : {22,22}
Number of vertices, edges, etc : 22, 242, 22
Order of s₀s₁s₂ : 22
Order of s₀s₁s₂s₁ : 22
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {22,22,2} of size 1936
Vertex Figure Of :
   {2,22,22} of size 1936
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {11,22}*484
   11-fold quotients : {22,2}*88
   22-fold quotients : {11,2}*44
   121-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {44,22}*1936b, {22,44}*1936c
Permutation Representation (GAP) :

s0 := (  2, 11)(  3, 10)(  4,  9)(  5,  8)(  6,  7)( 12,111)( 13,121)( 14,120)
( 15,119)( 16,118)( 17,117)( 18,116)( 19,115)( 20,114)( 21,113)( 22,112)
( 23,100)( 24,110)( 25,109)( 26,108)( 27,107)( 28,106)( 29,105)( 30,104)
( 31,103)( 32,102)( 33,101)( 34, 89)( 35, 99)( 36, 98)( 37, 97)( 38, 96)
( 39, 95)( 40, 94)( 41, 93)( 42, 92)( 43, 91)( 44, 90)( 45, 78)( 46, 88)
( 47, 87)( 48, 86)( 49, 85)( 50, 84)( 51, 83)( 52, 82)( 53, 81)( 54, 80)
( 55, 79)( 56, 67)( 57, 77)( 58, 76)( 59, 75)( 60, 74)( 61, 73)( 62, 72)
( 63, 71)( 64, 70)( 65, 69)( 66, 68)(123,132)(124,131)(125,130)(126,129)
(127,128)(133,232)(134,242)(135,241)(136,240)(137,239)(138,238)(139,237)
(140,236)(141,235)(142,234)(143,233)(144,221)(145,231)(146,230)(147,229)
(148,228)(149,227)(150,226)(151,225)(152,224)(153,223)(154,222)(155,210)
(156,220)(157,219)(158,218)(159,217)(160,216)(161,215)(162,214)(163,213)
(164,212)(165,211)(166,199)(167,209)(168,208)(169,207)(170,206)(171,205)
(172,204)(173,203)(174,202)(175,201)(176,200)(177,188)(178,198)(179,197)
(180,196)(181,195)(182,194)(183,193)(184,192)(185,191)(186,190)(187,189);;
s1 := (  1,134)(  2,133)(  3,143)(  4,142)(  5,141)(  6,140)(  7,139)(  8,138)
(  9,137)( 10,136)( 11,135)( 12,123)( 13,122)( 14,132)( 15,131)( 16,130)
( 17,129)( 18,128)( 19,127)( 20,126)( 21,125)( 22,124)( 23,233)( 24,232)
( 25,242)( 26,241)( 27,240)( 28,239)( 29,238)( 30,237)( 31,236)( 32,235)
( 33,234)( 34,222)( 35,221)( 36,231)( 37,230)( 38,229)( 39,228)( 40,227)
( 41,226)( 42,225)( 43,224)( 44,223)( 45,211)( 46,210)( 47,220)( 48,219)
( 49,218)( 50,217)( 51,216)( 52,215)( 53,214)( 54,213)( 55,212)( 56,200)
( 57,199)( 58,209)( 59,208)( 60,207)( 61,206)( 62,205)( 63,204)( 64,203)
( 65,202)( 66,201)( 67,189)( 68,188)( 69,198)( 70,197)( 71,196)( 72,195)
( 73,194)( 74,193)( 75,192)( 76,191)( 77,190)( 78,178)( 79,177)( 80,187)
( 81,186)( 82,185)( 83,184)( 84,183)( 85,182)( 86,181)( 87,180)( 88,179)
( 89,167)( 90,166)( 91,176)( 92,175)( 93,174)( 94,173)( 95,172)( 96,171)
( 97,170)( 98,169)( 99,168)(100,156)(101,155)(102,165)(103,164)(104,163)
(105,162)(106,161)(107,160)(108,159)(109,158)(110,157)(111,145)(112,144)
(113,154)(114,153)(115,152)(116,151)(117,150)(118,149)(119,148)(120,147)
(121,146);;
s2 := (  2, 11)(  3, 10)(  4,  9)(  5,  8)(  6,  7)( 13, 22)( 14, 21)( 15, 20)
( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)( 35, 44)
( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 46, 55)( 47, 54)( 48, 53)( 49, 52)
( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 68, 77)( 69, 76)
( 70, 75)( 71, 74)( 72, 73)( 79, 88)( 80, 87)( 81, 86)( 82, 85)( 83, 84)
( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)(101,110)(102,109)(103,108)
(104,107)(105,106)(112,121)(113,120)(114,119)(115,118)(116,117)(123,132)
(124,131)(125,130)(126,129)(127,128)(134,143)(135,142)(136,141)(137,140)
(138,139)(145,154)(146,153)(147,152)(148,151)(149,150)(156,165)(157,164)
(158,163)(159,162)(160,161)(167,176)(168,175)(169,174)(170,173)(171,172)
(178,187)(179,186)(180,185)(181,184)(182,183)(189,198)(190,197)(191,196)
(192,195)(193,194)(200,209)(201,208)(202,207)(203,206)(204,205)(211,220)
(212,219)(213,218)(214,217)(215,216)(222,231)(223,230)(224,229)(225,228)
(226,227)(233,242)(234,241)(235,240)(236,239)(237,238);;
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, s2*s0*s1*s2*s1*s2*s0*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*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*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(242)!(  2, 11)(  3, 10)(  4,  9)(  5,  8)(  6,  7)( 12,111)( 13,121)
( 14,120)( 15,119)( 16,118)( 17,117)( 18,116)( 19,115)( 20,114)( 21,113)
( 22,112)( 23,100)( 24,110)( 25,109)( 26,108)( 27,107)( 28,106)( 29,105)
( 30,104)( 31,103)( 32,102)( 33,101)( 34, 89)( 35, 99)( 36, 98)( 37, 97)
( 38, 96)( 39, 95)( 40, 94)( 41, 93)( 42, 92)( 43, 91)( 44, 90)( 45, 78)
( 46, 88)( 47, 87)( 48, 86)( 49, 85)( 50, 84)( 51, 83)( 52, 82)( 53, 81)
( 54, 80)( 55, 79)( 56, 67)( 57, 77)( 58, 76)( 59, 75)( 60, 74)( 61, 73)
( 62, 72)( 63, 71)( 64, 70)( 65, 69)( 66, 68)(123,132)(124,131)(125,130)
(126,129)(127,128)(133,232)(134,242)(135,241)(136,240)(137,239)(138,238)
(139,237)(140,236)(141,235)(142,234)(143,233)(144,221)(145,231)(146,230)
(147,229)(148,228)(149,227)(150,226)(151,225)(152,224)(153,223)(154,222)
(155,210)(156,220)(157,219)(158,218)(159,217)(160,216)(161,215)(162,214)
(163,213)(164,212)(165,211)(166,199)(167,209)(168,208)(169,207)(170,206)
(171,205)(172,204)(173,203)(174,202)(175,201)(176,200)(177,188)(178,198)
(179,197)(180,196)(181,195)(182,194)(183,193)(184,192)(185,191)(186,190)
(187,189);
s1 := Sym(242)!(  1,134)(  2,133)(  3,143)(  4,142)(  5,141)(  6,140)(  7,139)
(  8,138)(  9,137)( 10,136)( 11,135)( 12,123)( 13,122)( 14,132)( 15,131)
( 16,130)( 17,129)( 18,128)( 19,127)( 20,126)( 21,125)( 22,124)( 23,233)
( 24,232)( 25,242)( 26,241)( 27,240)( 28,239)( 29,238)( 30,237)( 31,236)
( 32,235)( 33,234)( 34,222)( 35,221)( 36,231)( 37,230)( 38,229)( 39,228)
( 40,227)( 41,226)( 42,225)( 43,224)( 44,223)( 45,211)( 46,210)( 47,220)
( 48,219)( 49,218)( 50,217)( 51,216)( 52,215)( 53,214)( 54,213)( 55,212)
( 56,200)( 57,199)( 58,209)( 59,208)( 60,207)( 61,206)( 62,205)( 63,204)
( 64,203)( 65,202)( 66,201)( 67,189)( 68,188)( 69,198)( 70,197)( 71,196)
( 72,195)( 73,194)( 74,193)( 75,192)( 76,191)( 77,190)( 78,178)( 79,177)
( 80,187)( 81,186)( 82,185)( 83,184)( 84,183)( 85,182)( 86,181)( 87,180)
( 88,179)( 89,167)( 90,166)( 91,176)( 92,175)( 93,174)( 94,173)( 95,172)
( 96,171)( 97,170)( 98,169)( 99,168)(100,156)(101,155)(102,165)(103,164)
(104,163)(105,162)(106,161)(107,160)(108,159)(109,158)(110,157)(111,145)
(112,144)(113,154)(114,153)(115,152)(116,151)(117,150)(118,149)(119,148)
(120,147)(121,146);
s2 := Sym(242)!(  2, 11)(  3, 10)(  4,  9)(  5,  8)(  6,  7)( 13, 22)( 14, 21)
( 15, 20)( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)
( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 46, 55)( 47, 54)( 48, 53)
( 49, 52)( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 68, 77)
( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79, 88)( 80, 87)( 81, 86)( 82, 85)
( 83, 84)( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)(101,110)(102,109)
(103,108)(104,107)(105,106)(112,121)(113,120)(114,119)(115,118)(116,117)
(123,132)(124,131)(125,130)(126,129)(127,128)(134,143)(135,142)(136,141)
(137,140)(138,139)(145,154)(146,153)(147,152)(148,151)(149,150)(156,165)
(157,164)(158,163)(159,162)(160,161)(167,176)(168,175)(169,174)(170,173)
(171,172)(178,187)(179,186)(180,185)(181,184)(182,183)(189,198)(190,197)
(191,196)(192,195)(193,194)(200,209)(201,208)(202,207)(203,206)(204,205)
(211,220)(212,219)(213,218)(214,217)(215,216)(222,231)(223,230)(224,229)
(225,228)(226,227)(233,242)(234,241)(235,240)(236,239)(237,238);
poly := sub<Sym(242)|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, s2*s0*s1*s2*s1*s2*s0*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*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope