Polytope of Type {10,65}

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