Polytope of Type {52,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {52,10}*1040
Also Known As : {52,10|2}. if this polytope has another name.
Group : SmallGroup(1040,167)
Rank : 3
Schlafli Type : {52,10}
Number of vertices, edges, etc : 52, 260, 10
Order of s₀s₁s₂ : 260
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {26,10}*520
   5-fold quotients : {52,2}*208
   10-fold quotients : {26,2}*104
   13-fold quotients : {4,10}*80
   20-fold quotients : {13,2}*52
   26-fold quotients : {2,10}*40
   52-fold quotients : {2,5}*20
   65-fold quotients : {4,2}*16
   130-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 13)(  3, 12)(  4, 11)(  5, 10)(  6,  9)(  7,  8)( 15, 26)( 16, 25)
( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 28, 39)( 29, 38)( 30, 37)( 31, 36)
( 32, 35)( 33, 34)( 41, 52)( 42, 51)( 43, 50)( 44, 49)( 45, 48)( 46, 47)
( 54, 65)( 55, 64)( 56, 63)( 57, 62)( 58, 61)( 59, 60)( 67, 78)( 68, 77)
( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 80, 91)( 81, 90)( 82, 89)( 83, 88)
( 84, 87)( 85, 86)( 93,104)( 94,103)( 95,102)( 96,101)( 97,100)( 98, 99)
(106,117)(107,116)(108,115)(109,114)(110,113)(111,112)(119,130)(120,129)
(121,128)(122,127)(123,126)(124,125)(131,196)(132,208)(133,207)(134,206)
(135,205)(136,204)(137,203)(138,202)(139,201)(140,200)(141,199)(142,198)
(143,197)(144,209)(145,221)(146,220)(147,219)(148,218)(149,217)(150,216)
(151,215)(152,214)(153,213)(154,212)(155,211)(156,210)(157,222)(158,234)
(159,233)(160,232)(161,231)(162,230)(163,229)(164,228)(165,227)(166,226)
(167,225)(168,224)(169,223)(170,235)(171,247)(172,246)(173,245)(174,244)
(175,243)(176,242)(177,241)(178,240)(179,239)(180,238)(181,237)(182,236)
(183,248)(184,260)(185,259)(186,258)(187,257)(188,256)(189,255)(190,254)
(191,253)(192,252)(193,251)(194,250)(195,249);;
s1 := (  1,132)(  2,131)(  3,143)(  4,142)(  5,141)(  6,140)(  7,139)(  8,138)
(  9,137)( 10,136)( 11,135)( 12,134)( 13,133)( 14,184)( 15,183)( 16,195)
( 17,194)( 18,193)( 19,192)( 20,191)( 21,190)( 22,189)( 23,188)( 24,187)
( 25,186)( 26,185)( 27,171)( 28,170)( 29,182)( 30,181)( 31,180)( 32,179)
( 33,178)( 34,177)( 35,176)( 36,175)( 37,174)( 38,173)( 39,172)( 40,158)
( 41,157)( 42,169)( 43,168)( 44,167)( 45,166)( 46,165)( 47,164)( 48,163)
( 49,162)( 50,161)( 51,160)( 52,159)( 53,145)( 54,144)( 55,156)( 56,155)
( 57,154)( 58,153)( 59,152)( 60,151)( 61,150)( 62,149)( 63,148)( 64,147)
( 65,146)( 66,197)( 67,196)( 68,208)( 69,207)( 70,206)( 71,205)( 72,204)
( 73,203)( 74,202)( 75,201)( 76,200)( 77,199)( 78,198)( 79,249)( 80,248)
( 81,260)( 82,259)( 83,258)( 84,257)( 85,256)( 86,255)( 87,254)( 88,253)
( 89,252)( 90,251)( 91,250)( 92,236)( 93,235)( 94,247)( 95,246)( 96,245)
( 97,244)( 98,243)( 99,242)(100,241)(101,240)(102,239)(103,238)(104,237)
(105,223)(106,222)(107,234)(108,233)(109,232)(110,231)(111,230)(112,229)
(113,228)(114,227)(115,226)(116,225)(117,224)(118,210)(119,209)(120,221)
(121,220)(122,219)(123,218)(124,217)(125,216)(126,215)(127,214)(128,213)
(129,212)(130,211);;
s2 := (  1, 14)(  2, 15)(  3, 16)(  4, 17)(  5, 18)(  6, 19)(  7, 20)(  8, 21)
(  9, 22)( 10, 23)( 11, 24)( 12, 25)( 13, 26)( 27, 53)( 28, 54)( 29, 55)
( 30, 56)( 31, 57)( 32, 58)( 33, 59)( 34, 60)( 35, 61)( 36, 62)( 37, 63)
( 38, 64)( 39, 65)( 66, 79)( 67, 80)( 68, 81)( 69, 82)( 70, 83)( 71, 84)
( 72, 85)( 73, 86)( 74, 87)( 75, 88)( 76, 89)( 77, 90)( 78, 91)( 92,118)
( 93,119)( 94,120)( 95,121)( 96,122)( 97,123)( 98,124)( 99,125)(100,126)
(101,127)(102,128)(103,129)(104,130)(131,144)(132,145)(133,146)(134,147)
(135,148)(136,149)(137,150)(138,151)(139,152)(140,153)(141,154)(142,155)
(143,156)(157,183)(158,184)(159,185)(160,186)(161,187)(162,188)(163,189)
(164,190)(165,191)(166,192)(167,193)(168,194)(169,195)(196,209)(197,210)
(198,211)(199,212)(200,213)(201,214)(202,215)(203,216)(204,217)(205,218)
(206,219)(207,220)(208,221)(222,248)(223,249)(224,250)(225,251)(226,252)
(227,253)(228,254)(229,255)(230,256)(231,257)(232,258)(233,259)(234,260);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(260)!(  2, 13)(  3, 12)(  4, 11)(  5, 10)(  6,  9)(  7,  8)( 15, 26)
( 16, 25)( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 28, 39)( 29, 38)( 30, 37)
( 31, 36)( 32, 35)( 33, 34)( 41, 52)( 42, 51)( 43, 50)( 44, 49)( 45, 48)
( 46, 47)( 54, 65)( 55, 64)( 56, 63)( 57, 62)( 58, 61)( 59, 60)( 67, 78)
( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 80, 91)( 81, 90)( 82, 89)
( 83, 88)( 84, 87)( 85, 86)( 93,104)( 94,103)( 95,102)( 96,101)( 97,100)
( 98, 99)(106,117)(107,116)(108,115)(109,114)(110,113)(111,112)(119,130)
(120,129)(121,128)(122,127)(123,126)(124,125)(131,196)(132,208)(133,207)
(134,206)(135,205)(136,204)(137,203)(138,202)(139,201)(140,200)(141,199)
(142,198)(143,197)(144,209)(145,221)(146,220)(147,219)(148,218)(149,217)
(150,216)(151,215)(152,214)(153,213)(154,212)(155,211)(156,210)(157,222)
(158,234)(159,233)(160,232)(161,231)(162,230)(163,229)(164,228)(165,227)
(166,226)(167,225)(168,224)(169,223)(170,235)(171,247)(172,246)(173,245)
(174,244)(175,243)(176,242)(177,241)(178,240)(179,239)(180,238)(181,237)
(182,236)(183,248)(184,260)(185,259)(186,258)(187,257)(188,256)(189,255)
(190,254)(191,253)(192,252)(193,251)(194,250)(195,249);
s1 := Sym(260)!(  1,132)(  2,131)(  3,143)(  4,142)(  5,141)(  6,140)(  7,139)
(  8,138)(  9,137)( 10,136)( 11,135)( 12,134)( 13,133)( 14,184)( 15,183)
( 16,195)( 17,194)( 18,193)( 19,192)( 20,191)( 21,190)( 22,189)( 23,188)
( 24,187)( 25,186)( 26,185)( 27,171)( 28,170)( 29,182)( 30,181)( 31,180)
( 32,179)( 33,178)( 34,177)( 35,176)( 36,175)( 37,174)( 38,173)( 39,172)
( 40,158)( 41,157)( 42,169)( 43,168)( 44,167)( 45,166)( 46,165)( 47,164)
( 48,163)( 49,162)( 50,161)( 51,160)( 52,159)( 53,145)( 54,144)( 55,156)
( 56,155)( 57,154)( 58,153)( 59,152)( 60,151)( 61,150)( 62,149)( 63,148)
( 64,147)( 65,146)( 66,197)( 67,196)( 68,208)( 69,207)( 70,206)( 71,205)
( 72,204)( 73,203)( 74,202)( 75,201)( 76,200)( 77,199)( 78,198)( 79,249)
( 80,248)( 81,260)( 82,259)( 83,258)( 84,257)( 85,256)( 86,255)( 87,254)
( 88,253)( 89,252)( 90,251)( 91,250)( 92,236)( 93,235)( 94,247)( 95,246)
( 96,245)( 97,244)( 98,243)( 99,242)(100,241)(101,240)(102,239)(103,238)
(104,237)(105,223)(106,222)(107,234)(108,233)(109,232)(110,231)(111,230)
(112,229)(113,228)(114,227)(115,226)(116,225)(117,224)(118,210)(119,209)
(120,221)(121,220)(122,219)(123,218)(124,217)(125,216)(126,215)(127,214)
(128,213)(129,212)(130,211);
s2 := Sym(260)!(  1, 14)(  2, 15)(  3, 16)(  4, 17)(  5, 18)(  6, 19)(  7, 20)
(  8, 21)(  9, 22)( 10, 23)( 11, 24)( 12, 25)( 13, 26)( 27, 53)( 28, 54)
( 29, 55)( 30, 56)( 31, 57)( 32, 58)( 33, 59)( 34, 60)( 35, 61)( 36, 62)
( 37, 63)( 38, 64)( 39, 65)( 66, 79)( 67, 80)( 68, 81)( 69, 82)( 70, 83)
( 71, 84)( 72, 85)( 73, 86)( 74, 87)( 75, 88)( 76, 89)( 77, 90)( 78, 91)
( 92,118)( 93,119)( 94,120)( 95,121)( 96,122)( 97,123)( 98,124)( 99,125)
(100,126)(101,127)(102,128)(103,129)(104,130)(131,144)(132,145)(133,146)
(134,147)(135,148)(136,149)(137,150)(138,151)(139,152)(140,153)(141,154)
(142,155)(143,156)(157,183)(158,184)(159,185)(160,186)(161,187)(162,188)
(163,189)(164,190)(165,191)(166,192)(167,193)(168,194)(169,195)(196,209)
(197,210)(198,211)(199,212)(200,213)(201,214)(202,215)(203,216)(204,217)
(205,218)(206,219)(207,220)(208,221)(222,248)(223,249)(224,250)(225,251)
(226,252)(227,253)(228,254)(229,255)(230,256)(231,257)(232,258)(233,259)
(234,260);
poly := sub<Sym(260)|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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope