Polytope of Type {10,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,12}*1200a
if this polytope has a name.
Group : SmallGroup(1200,514)
Rank : 3
Schlafli Type : {10,12}
Number of vertices, edges, etc : 50, 300, 60
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 : {10,6}*600b
   4-fold quotients : {10,3}*300
   25-fold quotients : {2,12}*48
   50-fold quotients : {2,6}*24
   75-fold quotients : {2,4}*16
   100-fold quotients : {2,3}*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, 21)(  7, 25)(  8, 24)(  9, 23)( 10, 22)( 11, 16)
( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 27, 30)( 28, 29)( 31, 46)( 32, 50)
( 33, 49)( 34, 48)( 35, 47)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)
( 52, 55)( 53, 54)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)( 61, 66)
( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 77, 80)( 78, 79)( 81, 96)( 82,100)
( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)( 89, 93)( 90, 92)
(102,105)(103,104)(106,121)(107,125)(108,124)(109,123)(110,122)(111,116)
(112,120)(113,119)(114,118)(115,117)(127,130)(128,129)(131,146)(132,150)
(133,149)(134,148)(135,147)(136,141)(137,145)(138,144)(139,143)(140,142)
(152,155)(153,154)(156,171)(157,175)(158,174)(159,173)(160,172)(161,166)
(162,170)(163,169)(164,168)(165,167)(177,180)(178,179)(181,196)(182,200)
(183,199)(184,198)(185,197)(186,191)(187,195)(188,194)(189,193)(190,192)
(202,205)(203,204)(206,221)(207,225)(208,224)(209,223)(210,222)(211,216)
(212,220)(213,219)(214,218)(215,217)(227,230)(228,229)(231,246)(232,250)
(233,249)(234,248)(235,247)(236,241)(237,245)(238,244)(239,243)(240,242)
(252,255)(253,254)(256,271)(257,275)(258,274)(259,273)(260,272)(261,266)
(262,270)(263,269)(264,268)(265,267)(277,280)(278,279)(281,296)(282,300)
(283,299)(284,298)(285,297)(286,291)(287,295)(288,294)(289,293)(290,292);;
s1 := (  1,  2)(  3,  5)(  6,  8)(  9, 10)( 11, 14)( 12, 13)( 16, 20)( 17, 19)
( 22, 25)( 23, 24)( 26, 52)( 27, 51)( 28, 55)( 29, 54)( 30, 53)( 31, 58)
( 32, 57)( 33, 56)( 34, 60)( 35, 59)( 36, 64)( 37, 63)( 38, 62)( 39, 61)
( 40, 65)( 41, 70)( 42, 69)( 43, 68)( 44, 67)( 45, 66)( 46, 71)( 47, 75)
( 48, 74)( 49, 73)( 50, 72)( 76, 77)( 78, 80)( 81, 83)( 84, 85)( 86, 89)
( 87, 88)( 91, 95)( 92, 94)( 97,100)( 98, 99)(101,127)(102,126)(103,130)
(104,129)(105,128)(106,133)(107,132)(108,131)(109,135)(110,134)(111,139)
(112,138)(113,137)(114,136)(115,140)(116,145)(117,144)(118,143)(119,142)
(120,141)(121,146)(122,150)(123,149)(124,148)(125,147)(151,227)(152,226)
(153,230)(154,229)(155,228)(156,233)(157,232)(158,231)(159,235)(160,234)
(161,239)(162,238)(163,237)(164,236)(165,240)(166,245)(167,244)(168,243)
(169,242)(170,241)(171,246)(172,250)(173,249)(174,248)(175,247)(176,277)
(177,276)(178,280)(179,279)(180,278)(181,283)(182,282)(183,281)(184,285)
(185,284)(186,289)(187,288)(188,287)(189,286)(190,290)(191,295)(192,294)
(193,293)(194,292)(195,291)(196,296)(197,300)(198,299)(199,298)(200,297)
(201,252)(202,251)(203,255)(204,254)(205,253)(206,258)(207,257)(208,256)
(209,260)(210,259)(211,264)(212,263)(213,262)(214,261)(215,265)(216,270)
(217,269)(218,268)(219,267)(220,266)(221,271)(222,275)(223,274)(224,273)
(225,272);;
s2 := (  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);;
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*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope