Polytope of Type {6,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,20}*1200b
if this polytope has a name.
Group : SmallGroup(1200,522)
Rank : 3
Schlafli Type : {6,20}
Number of vertices, edges, etc : 30, 300, 100
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {6,10}*600b
   4-fold quotients : {3,10}*300
   25-fold quotients : {6,4}*48a
   50-fold quotients : {6,2}*24
   75-fold quotients : {2,4}*16
   100-fold quotients : {3,2}*12
   150-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,  5)(  3,  4)(  6,  7)(  8, 10)( 11, 13)( 14, 15)( 16, 19)( 17, 18)
( 21, 25)( 22, 24)( 26, 51)( 27, 55)( 28, 54)( 29, 53)( 30, 52)( 31, 57)
( 32, 56)( 33, 60)( 34, 59)( 35, 58)( 36, 63)( 37, 62)( 38, 61)( 39, 65)
( 40, 64)( 41, 69)( 42, 68)( 43, 67)( 44, 66)( 45, 70)( 46, 75)( 47, 74)
( 48, 73)( 49, 72)( 50, 71)( 77, 80)( 78, 79)( 81, 82)( 83, 85)( 86, 88)
( 89, 90)( 91, 94)( 92, 93)( 96,100)( 97, 99)(101,126)(102,130)(103,129)
(104,128)(105,127)(106,132)(107,131)(108,135)(109,134)(110,133)(111,138)
(112,137)(113,136)(114,140)(115,139)(116,144)(117,143)(118,142)(119,141)
(120,145)(121,150)(122,149)(123,148)(124,147)(125,146)(152,155)(153,154)
(156,157)(158,160)(161,163)(164,165)(166,169)(167,168)(171,175)(172,174)
(176,201)(177,205)(178,204)(179,203)(180,202)(181,207)(182,206)(183,210)
(184,209)(185,208)(186,213)(187,212)(188,211)(189,215)(190,214)(191,219)
(192,218)(193,217)(194,216)(195,220)(196,225)(197,224)(198,223)(199,222)
(200,221)(227,230)(228,229)(231,232)(233,235)(236,238)(239,240)(241,244)
(242,243)(246,250)(247,249)(251,276)(252,280)(253,279)(254,278)(255,277)
(256,282)(257,281)(258,285)(259,284)(260,283)(261,288)(262,287)(263,286)
(264,290)(265,289)(266,294)(267,293)(268,292)(269,291)(270,295)(271,300)
(272,299)(273,298)(274,297)(275,296);;
s1 := (  1,176)(  2,182)(  3,188)(  4,194)(  5,200)(  6,196)(  7,177)(  8,183)
(  9,189)( 10,195)( 11,191)( 12,197)( 13,178)( 14,184)( 15,190)( 16,186)
( 17,192)( 18,198)( 19,179)( 20,185)( 21,181)( 22,187)( 23,193)( 24,199)
( 25,180)( 26,151)( 27,157)( 28,163)( 29,169)( 30,175)( 31,171)( 32,152)
( 33,158)( 34,164)( 35,170)( 36,166)( 37,172)( 38,153)( 39,159)( 40,165)
( 41,161)( 42,167)( 43,173)( 44,154)( 45,160)( 46,156)( 47,162)( 48,168)
( 49,174)( 50,155)( 51,201)( 52,207)( 53,213)( 54,219)( 55,225)( 56,221)
( 57,202)( 58,208)( 59,214)( 60,220)( 61,216)( 62,222)( 63,203)( 64,209)
( 65,215)( 66,211)( 67,217)( 68,223)( 69,204)( 70,210)( 71,206)( 72,212)
( 73,218)( 74,224)( 75,205)( 76,251)( 77,257)( 78,263)( 79,269)( 80,275)
( 81,271)( 82,252)( 83,258)( 84,264)( 85,270)( 86,266)( 87,272)( 88,253)
( 89,259)( 90,265)( 91,261)( 92,267)( 93,273)( 94,254)( 95,260)( 96,256)
( 97,262)( 98,268)( 99,274)(100,255)(101,226)(102,232)(103,238)(104,244)
(105,250)(106,246)(107,227)(108,233)(109,239)(110,245)(111,241)(112,247)
(113,228)(114,234)(115,240)(116,236)(117,242)(118,248)(119,229)(120,235)
(121,231)(122,237)(123,243)(124,249)(125,230)(126,276)(127,282)(128,288)
(129,294)(130,300)(131,296)(132,277)(133,283)(134,289)(135,295)(136,291)
(137,297)(138,278)(139,284)(140,290)(141,286)(142,292)(143,298)(144,279)
(145,285)(146,281)(147,287)(148,293)(149,299)(150,280);;
s2 := (  1, 12)(  2, 11)(  3, 15)(  4, 14)(  5, 13)(  6,  7)(  8, 10)( 16, 22)
( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 37)( 27, 36)( 28, 40)( 29, 39)
( 30, 38)( 31, 32)( 33, 35)( 41, 47)( 42, 46)( 43, 50)( 44, 49)( 45, 48)
( 51, 62)( 52, 61)( 53, 65)( 54, 64)( 55, 63)( 56, 57)( 58, 60)( 66, 72)
( 67, 71)( 68, 75)( 69, 74)( 70, 73)( 76, 87)( 77, 86)( 78, 90)( 79, 89)
( 80, 88)( 81, 82)( 83, 85)( 91, 97)( 92, 96)( 93,100)( 94, 99)( 95, 98)
(101,112)(102,111)(103,115)(104,114)(105,113)(106,107)(108,110)(116,122)
(117,121)(118,125)(119,124)(120,123)(126,137)(127,136)(128,140)(129,139)
(130,138)(131,132)(133,135)(141,147)(142,146)(143,150)(144,149)(145,148)
(151,237)(152,236)(153,240)(154,239)(155,238)(156,232)(157,231)(158,235)
(159,234)(160,233)(161,227)(162,226)(163,230)(164,229)(165,228)(166,247)
(167,246)(168,250)(169,249)(170,248)(171,242)(172,241)(173,245)(174,244)
(175,243)(176,262)(177,261)(178,265)(179,264)(180,263)(181,257)(182,256)
(183,260)(184,259)(185,258)(186,252)(187,251)(188,255)(189,254)(190,253)
(191,272)(192,271)(193,275)(194,274)(195,273)(196,267)(197,266)(198,270)
(199,269)(200,268)(201,287)(202,286)(203,290)(204,289)(205,288)(206,282)
(207,281)(208,285)(209,284)(210,283)(211,277)(212,276)(213,280)(214,279)
(215,278)(216,297)(217,296)(218,300)(219,299)(220,298)(221,292)(222,291)
(223,295)(224,294)(225,293);;
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, 
s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(300)!(  2,  5)(  3,  4)(  6,  7)(  8, 10)( 11, 13)( 14, 15)( 16, 19)
( 17, 18)( 21, 25)( 22, 24)( 26, 51)( 27, 55)( 28, 54)( 29, 53)( 30, 52)
( 31, 57)( 32, 56)( 33, 60)( 34, 59)( 35, 58)( 36, 63)( 37, 62)( 38, 61)
( 39, 65)( 40, 64)( 41, 69)( 42, 68)( 43, 67)( 44, 66)( 45, 70)( 46, 75)
( 47, 74)( 48, 73)( 49, 72)( 50, 71)( 77, 80)( 78, 79)( 81, 82)( 83, 85)
( 86, 88)( 89, 90)( 91, 94)( 92, 93)( 96,100)( 97, 99)(101,126)(102,130)
(103,129)(104,128)(105,127)(106,132)(107,131)(108,135)(109,134)(110,133)
(111,138)(112,137)(113,136)(114,140)(115,139)(116,144)(117,143)(118,142)
(119,141)(120,145)(121,150)(122,149)(123,148)(124,147)(125,146)(152,155)
(153,154)(156,157)(158,160)(161,163)(164,165)(166,169)(167,168)(171,175)
(172,174)(176,201)(177,205)(178,204)(179,203)(180,202)(181,207)(182,206)
(183,210)(184,209)(185,208)(186,213)(187,212)(188,211)(189,215)(190,214)
(191,219)(192,218)(193,217)(194,216)(195,220)(196,225)(197,224)(198,223)
(199,222)(200,221)(227,230)(228,229)(231,232)(233,235)(236,238)(239,240)
(241,244)(242,243)(246,250)(247,249)(251,276)(252,280)(253,279)(254,278)
(255,277)(256,282)(257,281)(258,285)(259,284)(260,283)(261,288)(262,287)
(263,286)(264,290)(265,289)(266,294)(267,293)(268,292)(269,291)(270,295)
(271,300)(272,299)(273,298)(274,297)(275,296);
s1 := Sym(300)!(  1,176)(  2,182)(  3,188)(  4,194)(  5,200)(  6,196)(  7,177)
(  8,183)(  9,189)( 10,195)( 11,191)( 12,197)( 13,178)( 14,184)( 15,190)
( 16,186)( 17,192)( 18,198)( 19,179)( 20,185)( 21,181)( 22,187)( 23,193)
( 24,199)( 25,180)( 26,151)( 27,157)( 28,163)( 29,169)( 30,175)( 31,171)
( 32,152)( 33,158)( 34,164)( 35,170)( 36,166)( 37,172)( 38,153)( 39,159)
( 40,165)( 41,161)( 42,167)( 43,173)( 44,154)( 45,160)( 46,156)( 47,162)
( 48,168)( 49,174)( 50,155)( 51,201)( 52,207)( 53,213)( 54,219)( 55,225)
( 56,221)( 57,202)( 58,208)( 59,214)( 60,220)( 61,216)( 62,222)( 63,203)
( 64,209)( 65,215)( 66,211)( 67,217)( 68,223)( 69,204)( 70,210)( 71,206)
( 72,212)( 73,218)( 74,224)( 75,205)( 76,251)( 77,257)( 78,263)( 79,269)
( 80,275)( 81,271)( 82,252)( 83,258)( 84,264)( 85,270)( 86,266)( 87,272)
( 88,253)( 89,259)( 90,265)( 91,261)( 92,267)( 93,273)( 94,254)( 95,260)
( 96,256)( 97,262)( 98,268)( 99,274)(100,255)(101,226)(102,232)(103,238)
(104,244)(105,250)(106,246)(107,227)(108,233)(109,239)(110,245)(111,241)
(112,247)(113,228)(114,234)(115,240)(116,236)(117,242)(118,248)(119,229)
(120,235)(121,231)(122,237)(123,243)(124,249)(125,230)(126,276)(127,282)
(128,288)(129,294)(130,300)(131,296)(132,277)(133,283)(134,289)(135,295)
(136,291)(137,297)(138,278)(139,284)(140,290)(141,286)(142,292)(143,298)
(144,279)(145,285)(146,281)(147,287)(148,293)(149,299)(150,280);
s2 := Sym(300)!(  1, 12)(  2, 11)(  3, 15)(  4, 14)(  5, 13)(  6,  7)(  8, 10)
( 16, 22)( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 37)( 27, 36)( 28, 40)
( 29, 39)( 30, 38)( 31, 32)( 33, 35)( 41, 47)( 42, 46)( 43, 50)( 44, 49)
( 45, 48)( 51, 62)( 52, 61)( 53, 65)( 54, 64)( 55, 63)( 56, 57)( 58, 60)
( 66, 72)( 67, 71)( 68, 75)( 69, 74)( 70, 73)( 76, 87)( 77, 86)( 78, 90)
( 79, 89)( 80, 88)( 81, 82)( 83, 85)( 91, 97)( 92, 96)( 93,100)( 94, 99)
( 95, 98)(101,112)(102,111)(103,115)(104,114)(105,113)(106,107)(108,110)
(116,122)(117,121)(118,125)(119,124)(120,123)(126,137)(127,136)(128,140)
(129,139)(130,138)(131,132)(133,135)(141,147)(142,146)(143,150)(144,149)
(145,148)(151,237)(152,236)(153,240)(154,239)(155,238)(156,232)(157,231)
(158,235)(159,234)(160,233)(161,227)(162,226)(163,230)(164,229)(165,228)
(166,247)(167,246)(168,250)(169,249)(170,248)(171,242)(172,241)(173,245)
(174,244)(175,243)(176,262)(177,261)(178,265)(179,264)(180,263)(181,257)
(182,256)(183,260)(184,259)(185,258)(186,252)(187,251)(188,255)(189,254)
(190,253)(191,272)(192,271)(193,275)(194,274)(195,273)(196,267)(197,266)
(198,270)(199,269)(200,268)(201,287)(202,286)(203,290)(204,289)(205,288)
(206,282)(207,281)(208,285)(209,284)(210,283)(211,277)(212,276)(213,280)
(214,279)(215,278)(216,297)(217,296)(218,300)(219,299)(220,298)(221,292)
(222,291)(223,295)(224,294)(225,293);
poly := sub<Sym(300)|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, 
s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1 >;

References : None.
to this polytope