Polytope of Type {65,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {65,10}*1300
if this polytope has a name.
Group : SmallGroup(1300,43)
Rank : 3
Schlafli Type : {65,10}
Number of vertices, edges, etc : 65, 325, 10
Order of s₀s₁s₂ : 130
Order of s₀s₁s₂s₁ : 10
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) :
   5-fold quotients : {65,2}*260
   13-fold quotients : {5,10}*100
   25-fold quotients : {13,2}*52
   65-fold quotients : {5,2}*20
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)( 14, 53)( 15, 65)
( 16, 64)( 17, 63)( 18, 62)( 19, 61)( 20, 60)( 21, 59)( 22, 58)( 23, 57)
( 24, 56)( 25, 55)( 26, 54)( 27, 40)( 28, 52)( 29, 51)( 30, 50)( 31, 49)
( 32, 48)( 33, 47)( 34, 46)( 35, 45)( 36, 44)( 37, 43)( 38, 42)( 39, 41)
( 66,261)( 67,273)( 68,272)( 69,271)( 70,270)( 71,269)( 72,268)( 73,267)
( 74,266)( 75,265)( 76,264)( 77,263)( 78,262)( 79,313)( 80,325)( 81,324)
( 82,323)( 83,322)( 84,321)( 85,320)( 86,319)( 87,318)( 88,317)( 89,316)
( 90,315)( 91,314)( 92,300)( 93,312)( 94,311)( 95,310)( 96,309)( 97,308)
( 98,307)( 99,306)(100,305)(101,304)(102,303)(103,302)(104,301)(105,287)
(106,299)(107,298)(108,297)(109,296)(110,295)(111,294)(112,293)(113,292)
(114,291)(115,290)(116,289)(117,288)(118,274)(119,286)(120,285)(121,284)
(122,283)(123,282)(124,281)(125,280)(126,279)(127,278)(128,277)(129,276)
(130,275)(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)(144,248)(145,260)
(146,259)(147,258)(148,257)(149,256)(150,255)(151,254)(152,253)(153,252)
(154,251)(155,250)(156,249)(157,235)(158,247)(159,246)(160,245)(161,244)
(162,243)(163,242)(164,241)(165,240)(166,239)(167,238)(168,237)(169,236)
(170,222)(171,234)(172,233)(173,232)(174,231)(175,230)(176,229)(177,228)
(178,227)(179,226)(180,225)(181,224)(182,223)(183,209)(184,221)(185,220)
(186,219)(187,218)(188,217)(189,216)(190,215)(191,214)(192,213)(193,212)
(194,211)(195,210);;
s1 := (  1, 80)(  2, 79)(  3, 91)(  4, 90)(  5, 89)(  6, 88)(  7, 87)(  8, 86)
(  9, 85)( 10, 84)( 11, 83)( 12, 82)( 13, 81)( 14, 67)( 15, 66)( 16, 78)
( 17, 77)( 18, 76)( 19, 75)( 20, 74)( 21, 73)( 22, 72)( 23, 71)( 24, 70)
( 25, 69)( 26, 68)( 27,119)( 28,118)( 29,130)( 30,129)( 31,128)( 32,127)
( 33,126)( 34,125)( 35,124)( 36,123)( 37,122)( 38,121)( 39,120)( 40,106)
( 41,105)( 42,117)( 43,116)( 44,115)( 45,114)( 46,113)( 47,112)( 48,111)
( 49,110)( 50,109)( 51,108)( 52,107)( 53, 93)( 54, 92)( 55,104)( 56,103)
( 57,102)( 58,101)( 59,100)( 60, 99)( 61, 98)( 62, 97)( 63, 96)( 64, 95)
( 65, 94)(131,275)(132,274)(133,286)(134,285)(135,284)(136,283)(137,282)
(138,281)(139,280)(140,279)(141,278)(142,277)(143,276)(144,262)(145,261)
(146,273)(147,272)(148,271)(149,270)(150,269)(151,268)(152,267)(153,266)
(154,265)(155,264)(156,263)(157,314)(158,313)(159,325)(160,324)(161,323)
(162,322)(163,321)(164,320)(165,319)(166,318)(167,317)(168,316)(169,315)
(170,301)(171,300)(172,312)(173,311)(174,310)(175,309)(176,308)(177,307)
(178,306)(179,305)(180,304)(181,303)(182,302)(183,288)(184,287)(185,299)
(186,298)(187,297)(188,296)(189,295)(190,294)(191,293)(192,292)(193,291)
(194,290)(195,289)(196,210)(197,209)(198,221)(199,220)(200,219)(201,218)
(202,217)(203,216)(204,215)(205,214)(206,213)(207,212)(208,211)(222,249)
(223,248)(224,260)(225,259)(226,258)(227,257)(228,256)(229,255)(230,254)
(231,253)(232,252)(233,251)(234,250)(235,236)(237,247)(238,246)(239,245)
(240,244)(241,243);;
s2 := ( 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)
(274,313)(275,314)(276,315)(277,316)(278,317)(279,318)(280,319)(281,320)
(282,321)(283,322)(284,323)(285,324)(286,325)(287,300)(288,301)(289,302)
(290,303)(291,304)(292,305)(293,306)(294,307)(295,308)(296,309)(297,310)
(298,311)(299,312);;
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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*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*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(325)!(  2, 13)(  3, 12)(  4, 11)(  5, 10)(  6,  9)(  7,  8)( 14, 53)
( 15, 65)( 16, 64)( 17, 63)( 18, 62)( 19, 61)( 20, 60)( 21, 59)( 22, 58)
( 23, 57)( 24, 56)( 25, 55)( 26, 54)( 27, 40)( 28, 52)( 29, 51)( 30, 50)
( 31, 49)( 32, 48)( 33, 47)( 34, 46)( 35, 45)( 36, 44)( 37, 43)( 38, 42)
( 39, 41)( 66,261)( 67,273)( 68,272)( 69,271)( 70,270)( 71,269)( 72,268)
( 73,267)( 74,266)( 75,265)( 76,264)( 77,263)( 78,262)( 79,313)( 80,325)
( 81,324)( 82,323)( 83,322)( 84,321)( 85,320)( 86,319)( 87,318)( 88,317)
( 89,316)( 90,315)( 91,314)( 92,300)( 93,312)( 94,311)( 95,310)( 96,309)
( 97,308)( 98,307)( 99,306)(100,305)(101,304)(102,303)(103,302)(104,301)
(105,287)(106,299)(107,298)(108,297)(109,296)(110,295)(111,294)(112,293)
(113,292)(114,291)(115,290)(116,289)(117,288)(118,274)(119,286)(120,285)
(121,284)(122,283)(123,282)(124,281)(125,280)(126,279)(127,278)(128,277)
(129,276)(130,275)(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)(144,248)
(145,260)(146,259)(147,258)(148,257)(149,256)(150,255)(151,254)(152,253)
(153,252)(154,251)(155,250)(156,249)(157,235)(158,247)(159,246)(160,245)
(161,244)(162,243)(163,242)(164,241)(165,240)(166,239)(167,238)(168,237)
(169,236)(170,222)(171,234)(172,233)(173,232)(174,231)(175,230)(176,229)
(177,228)(178,227)(179,226)(180,225)(181,224)(182,223)(183,209)(184,221)
(185,220)(186,219)(187,218)(188,217)(189,216)(190,215)(191,214)(192,213)
(193,212)(194,211)(195,210);
s1 := Sym(325)!(  1, 80)(  2, 79)(  3, 91)(  4, 90)(  5, 89)(  6, 88)(  7, 87)
(  8, 86)(  9, 85)( 10, 84)( 11, 83)( 12, 82)( 13, 81)( 14, 67)( 15, 66)
( 16, 78)( 17, 77)( 18, 76)( 19, 75)( 20, 74)( 21, 73)( 22, 72)( 23, 71)
( 24, 70)( 25, 69)( 26, 68)( 27,119)( 28,118)( 29,130)( 30,129)( 31,128)
( 32,127)( 33,126)( 34,125)( 35,124)( 36,123)( 37,122)( 38,121)( 39,120)
( 40,106)( 41,105)( 42,117)( 43,116)( 44,115)( 45,114)( 46,113)( 47,112)
( 48,111)( 49,110)( 50,109)( 51,108)( 52,107)( 53, 93)( 54, 92)( 55,104)
( 56,103)( 57,102)( 58,101)( 59,100)( 60, 99)( 61, 98)( 62, 97)( 63, 96)
( 64, 95)( 65, 94)(131,275)(132,274)(133,286)(134,285)(135,284)(136,283)
(137,282)(138,281)(139,280)(140,279)(141,278)(142,277)(143,276)(144,262)
(145,261)(146,273)(147,272)(148,271)(149,270)(150,269)(151,268)(152,267)
(153,266)(154,265)(155,264)(156,263)(157,314)(158,313)(159,325)(160,324)
(161,323)(162,322)(163,321)(164,320)(165,319)(166,318)(167,317)(168,316)
(169,315)(170,301)(171,300)(172,312)(173,311)(174,310)(175,309)(176,308)
(177,307)(178,306)(179,305)(180,304)(181,303)(182,302)(183,288)(184,287)
(185,299)(186,298)(187,297)(188,296)(189,295)(190,294)(191,293)(192,292)
(193,291)(194,290)(195,289)(196,210)(197,209)(198,221)(199,220)(200,219)
(201,218)(202,217)(203,216)(204,215)(205,214)(206,213)(207,212)(208,211)
(222,249)(223,248)(224,260)(225,259)(226,258)(227,257)(228,256)(229,255)
(230,254)(231,253)(232,252)(233,251)(234,250)(235,236)(237,247)(238,246)
(239,245)(240,244)(241,243);
s2 := Sym(325)!( 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)(274,313)(275,314)(276,315)(277,316)(278,317)(279,318)(280,319)
(281,320)(282,321)(283,322)(284,323)(285,324)(286,325)(287,300)(288,301)
(289,302)(290,303)(291,304)(292,305)(293,306)(294,307)(295,308)(296,309)
(297,310)(298,311)(299,312);
poly := sub<Sym(325)|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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*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*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