Polytope of Type {10,52}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,52}*1040
Also Known As : {10,52|2}. if this polytope has another name.
Group : SmallGroup(1040,167)
Rank : 3
Schlafli Type : {10,52}
Number of vertices, edges, etc : 10, 260, 52
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 : {10,26}*520
   5-fold quotients : {2,52}*208
   10-fold quotients : {2,26}*104
   13-fold quotients : {10,4}*80
   20-fold quotients : {2,13}*52
   26-fold quotients : {10,2}*40
   52-fold quotients : {5,2}*20
   65-fold quotients : {2,4}*16
   130-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope