Polytope of Type {22,22}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,22}*968a
Also Known As : {22,22|2}. if this polytope has another 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 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Dual
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) :
   11-fold quotients : {2,22}*88, {22,2}*88
   22-fold quotients : {2,11}*44, {11,2}*44
   121-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {22,44}*1936a, {44,22}*1936a
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope