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Polytope of Type {2,32,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,32,10}*1280
if this polytope has a name.
Group : SmallGroup(1280,327682)
Rank : 4
Schlafli Type : {2,32,10}
Number of vertices, edges, etc : 2, 32, 160, 10
Order of s0s1s2s3 : 160
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   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 : {2,16,10}*640
   4-fold quotients : {2,8,10}*320
   5-fold quotients : {2,32,2}*256
   8-fold quotients : {2,4,10}*160
   10-fold quotients : {2,16,2}*128
   16-fold quotients : {2,2,10}*80
   20-fold quotients : {2,8,2}*64
   32-fold quotients : {2,2,5}*40
   40-fold quotients : {2,4,2}*32
   80-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 13, 18)( 14, 19)( 15, 20)( 16, 21)( 17, 22)( 23, 33)( 24, 34)( 25, 35)
( 26, 36)( 27, 37)( 28, 38)( 29, 39)( 30, 40)( 31, 41)( 32, 42)( 43, 63)
( 44, 64)( 45, 65)( 46, 66)( 47, 67)( 48, 68)( 49, 69)( 50, 70)( 51, 71)
( 52, 72)( 53, 78)( 54, 79)( 55, 80)( 56, 81)( 57, 82)( 58, 73)( 59, 74)
( 60, 75)( 61, 76)( 62, 77)( 93, 98)( 94, 99)( 95,100)( 96,101)( 97,102)
(103,113)(104,114)(105,115)(106,116)(107,117)(108,118)(109,119)(110,120)
(111,121)(112,122)(123,143)(124,144)(125,145)(126,146)(127,147)(128,148)
(129,149)(130,150)(131,151)(132,152)(133,158)(134,159)(135,160)(136,161)
(137,162)(138,153)(139,154)(140,155)(141,156)(142,157)(163,203)(164,204)
(165,205)(166,206)(167,207)(168,208)(169,209)(170,210)(171,211)(172,212)
(173,218)(174,219)(175,220)(176,221)(177,222)(178,213)(179,214)(180,215)
(181,216)(182,217)(183,233)(184,234)(185,235)(186,236)(187,237)(188,238)
(189,239)(190,240)(191,241)(192,242)(193,223)(194,224)(195,225)(196,226)
(197,227)(198,228)(199,229)(200,230)(201,231)(202,232)(243,283)(244,284)
(245,285)(246,286)(247,287)(248,288)(249,289)(250,290)(251,291)(252,292)
(253,298)(254,299)(255,300)(256,301)(257,302)(258,293)(259,294)(260,295)
(261,296)(262,297)(263,313)(264,314)(265,315)(266,316)(267,317)(268,318)
(269,319)(270,320)(271,321)(272,322)(273,303)(274,304)(275,305)(276,306)
(277,307)(278,308)(279,309)(280,310)(281,311)(282,312);;
s2 := (  3,243)(  4,247)(  5,246)(  6,245)(  7,244)(  8,248)(  9,252)( 10,251)
( 11,250)( 12,249)( 13,258)( 14,262)( 15,261)( 16,260)( 17,259)( 18,253)
( 19,257)( 20,256)( 21,255)( 22,254)( 23,273)( 24,277)( 25,276)( 26,275)
( 27,274)( 28,278)( 29,282)( 30,281)( 31,280)( 32,279)( 33,263)( 34,267)
( 35,266)( 36,265)( 37,264)( 38,268)( 39,272)( 40,271)( 41,270)( 42,269)
( 43,303)( 44,307)( 45,306)( 46,305)( 47,304)( 48,308)( 49,312)( 50,311)
( 51,310)( 52,309)( 53,318)( 54,322)( 55,321)( 56,320)( 57,319)( 58,313)
( 59,317)( 60,316)( 61,315)( 62,314)( 63,283)( 64,287)( 65,286)( 66,285)
( 67,284)( 68,288)( 69,292)( 70,291)( 71,290)( 72,289)( 73,298)( 74,302)
( 75,301)( 76,300)( 77,299)( 78,293)( 79,297)( 80,296)( 81,295)( 82,294)
( 83,163)( 84,167)( 85,166)( 86,165)( 87,164)( 88,168)( 89,172)( 90,171)
( 91,170)( 92,169)( 93,178)( 94,182)( 95,181)( 96,180)( 97,179)( 98,173)
( 99,177)(100,176)(101,175)(102,174)(103,193)(104,197)(105,196)(106,195)
(107,194)(108,198)(109,202)(110,201)(111,200)(112,199)(113,183)(114,187)
(115,186)(116,185)(117,184)(118,188)(119,192)(120,191)(121,190)(122,189)
(123,223)(124,227)(125,226)(126,225)(127,224)(128,228)(129,232)(130,231)
(131,230)(132,229)(133,238)(134,242)(135,241)(136,240)(137,239)(138,233)
(139,237)(140,236)(141,235)(142,234)(143,203)(144,207)(145,206)(146,205)
(147,204)(148,208)(149,212)(150,211)(151,210)(152,209)(153,218)(154,222)
(155,221)(156,220)(157,219)(158,213)(159,217)(160,216)(161,215)(162,214);;
s3 := (  3, 84)(  4, 83)(  5, 87)(  6, 86)(  7, 85)(  8, 89)(  9, 88)( 10, 92)
( 11, 91)( 12, 90)( 13, 94)( 14, 93)( 15, 97)( 16, 96)( 17, 95)( 18, 99)
( 19, 98)( 20,102)( 21,101)( 22,100)( 23,104)( 24,103)( 25,107)( 26,106)
( 27,105)( 28,109)( 29,108)( 30,112)( 31,111)( 32,110)( 33,114)( 34,113)
( 35,117)( 36,116)( 37,115)( 38,119)( 39,118)( 40,122)( 41,121)( 42,120)
( 43,124)( 44,123)( 45,127)( 46,126)( 47,125)( 48,129)( 49,128)( 50,132)
( 51,131)( 52,130)( 53,134)( 54,133)( 55,137)( 56,136)( 57,135)( 58,139)
( 59,138)( 60,142)( 61,141)( 62,140)( 63,144)( 64,143)( 65,147)( 66,146)
( 67,145)( 68,149)( 69,148)( 70,152)( 71,151)( 72,150)( 73,154)( 74,153)
( 75,157)( 76,156)( 77,155)( 78,159)( 79,158)( 80,162)( 81,161)( 82,160)
(163,244)(164,243)(165,247)(166,246)(167,245)(168,249)(169,248)(170,252)
(171,251)(172,250)(173,254)(174,253)(175,257)(176,256)(177,255)(178,259)
(179,258)(180,262)(181,261)(182,260)(183,264)(184,263)(185,267)(186,266)
(187,265)(188,269)(189,268)(190,272)(191,271)(192,270)(193,274)(194,273)
(195,277)(196,276)(197,275)(198,279)(199,278)(200,282)(201,281)(202,280)
(203,284)(204,283)(205,287)(206,286)(207,285)(208,289)(209,288)(210,292)
(211,291)(212,290)(213,294)(214,293)(215,297)(216,296)(217,295)(218,299)
(219,298)(220,302)(221,301)(222,300)(223,304)(224,303)(225,307)(226,306)
(227,305)(228,309)(229,308)(230,312)(231,311)(232,310)(233,314)(234,313)
(235,317)(236,316)(237,315)(238,319)(239,318)(240,322)(241,321)(242,320);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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(322)!(1,2);
s1 := Sym(322)!( 13, 18)( 14, 19)( 15, 20)( 16, 21)( 17, 22)( 23, 33)( 24, 34)
( 25, 35)( 26, 36)( 27, 37)( 28, 38)( 29, 39)( 30, 40)( 31, 41)( 32, 42)
( 43, 63)( 44, 64)( 45, 65)( 46, 66)( 47, 67)( 48, 68)( 49, 69)( 50, 70)
( 51, 71)( 52, 72)( 53, 78)( 54, 79)( 55, 80)( 56, 81)( 57, 82)( 58, 73)
( 59, 74)( 60, 75)( 61, 76)( 62, 77)( 93, 98)( 94, 99)( 95,100)( 96,101)
( 97,102)(103,113)(104,114)(105,115)(106,116)(107,117)(108,118)(109,119)
(110,120)(111,121)(112,122)(123,143)(124,144)(125,145)(126,146)(127,147)
(128,148)(129,149)(130,150)(131,151)(132,152)(133,158)(134,159)(135,160)
(136,161)(137,162)(138,153)(139,154)(140,155)(141,156)(142,157)(163,203)
(164,204)(165,205)(166,206)(167,207)(168,208)(169,209)(170,210)(171,211)
(172,212)(173,218)(174,219)(175,220)(176,221)(177,222)(178,213)(179,214)
(180,215)(181,216)(182,217)(183,233)(184,234)(185,235)(186,236)(187,237)
(188,238)(189,239)(190,240)(191,241)(192,242)(193,223)(194,224)(195,225)
(196,226)(197,227)(198,228)(199,229)(200,230)(201,231)(202,232)(243,283)
(244,284)(245,285)(246,286)(247,287)(248,288)(249,289)(250,290)(251,291)
(252,292)(253,298)(254,299)(255,300)(256,301)(257,302)(258,293)(259,294)
(260,295)(261,296)(262,297)(263,313)(264,314)(265,315)(266,316)(267,317)
(268,318)(269,319)(270,320)(271,321)(272,322)(273,303)(274,304)(275,305)
(276,306)(277,307)(278,308)(279,309)(280,310)(281,311)(282,312);
s2 := Sym(322)!(  3,243)(  4,247)(  5,246)(  6,245)(  7,244)(  8,248)(  9,252)
( 10,251)( 11,250)( 12,249)( 13,258)( 14,262)( 15,261)( 16,260)( 17,259)
( 18,253)( 19,257)( 20,256)( 21,255)( 22,254)( 23,273)( 24,277)( 25,276)
( 26,275)( 27,274)( 28,278)( 29,282)( 30,281)( 31,280)( 32,279)( 33,263)
( 34,267)( 35,266)( 36,265)( 37,264)( 38,268)( 39,272)( 40,271)( 41,270)
( 42,269)( 43,303)( 44,307)( 45,306)( 46,305)( 47,304)( 48,308)( 49,312)
( 50,311)( 51,310)( 52,309)( 53,318)( 54,322)( 55,321)( 56,320)( 57,319)
( 58,313)( 59,317)( 60,316)( 61,315)( 62,314)( 63,283)( 64,287)( 65,286)
( 66,285)( 67,284)( 68,288)( 69,292)( 70,291)( 71,290)( 72,289)( 73,298)
( 74,302)( 75,301)( 76,300)( 77,299)( 78,293)( 79,297)( 80,296)( 81,295)
( 82,294)( 83,163)( 84,167)( 85,166)( 86,165)( 87,164)( 88,168)( 89,172)
( 90,171)( 91,170)( 92,169)( 93,178)( 94,182)( 95,181)( 96,180)( 97,179)
( 98,173)( 99,177)(100,176)(101,175)(102,174)(103,193)(104,197)(105,196)
(106,195)(107,194)(108,198)(109,202)(110,201)(111,200)(112,199)(113,183)
(114,187)(115,186)(116,185)(117,184)(118,188)(119,192)(120,191)(121,190)
(122,189)(123,223)(124,227)(125,226)(126,225)(127,224)(128,228)(129,232)
(130,231)(131,230)(132,229)(133,238)(134,242)(135,241)(136,240)(137,239)
(138,233)(139,237)(140,236)(141,235)(142,234)(143,203)(144,207)(145,206)
(146,205)(147,204)(148,208)(149,212)(150,211)(151,210)(152,209)(153,218)
(154,222)(155,221)(156,220)(157,219)(158,213)(159,217)(160,216)(161,215)
(162,214);
s3 := Sym(322)!(  3, 84)(  4, 83)(  5, 87)(  6, 86)(  7, 85)(  8, 89)(  9, 88)
( 10, 92)( 11, 91)( 12, 90)( 13, 94)( 14, 93)( 15, 97)( 16, 96)( 17, 95)
( 18, 99)( 19, 98)( 20,102)( 21,101)( 22,100)( 23,104)( 24,103)( 25,107)
( 26,106)( 27,105)( 28,109)( 29,108)( 30,112)( 31,111)( 32,110)( 33,114)
( 34,113)( 35,117)( 36,116)( 37,115)( 38,119)( 39,118)( 40,122)( 41,121)
( 42,120)( 43,124)( 44,123)( 45,127)( 46,126)( 47,125)( 48,129)( 49,128)
( 50,132)( 51,131)( 52,130)( 53,134)( 54,133)( 55,137)( 56,136)( 57,135)
( 58,139)( 59,138)( 60,142)( 61,141)( 62,140)( 63,144)( 64,143)( 65,147)
( 66,146)( 67,145)( 68,149)( 69,148)( 70,152)( 71,151)( 72,150)( 73,154)
( 74,153)( 75,157)( 76,156)( 77,155)( 78,159)( 79,158)( 80,162)( 81,161)
( 82,160)(163,244)(164,243)(165,247)(166,246)(167,245)(168,249)(169,248)
(170,252)(171,251)(172,250)(173,254)(174,253)(175,257)(176,256)(177,255)
(178,259)(179,258)(180,262)(181,261)(182,260)(183,264)(184,263)(185,267)
(186,266)(187,265)(188,269)(189,268)(190,272)(191,271)(192,270)(193,274)
(194,273)(195,277)(196,276)(197,275)(198,279)(199,278)(200,282)(201,281)
(202,280)(203,284)(204,283)(205,287)(206,286)(207,285)(208,289)(209,288)
(210,292)(211,291)(212,290)(213,294)(214,293)(215,297)(216,296)(217,295)
(218,299)(219,298)(220,302)(221,301)(222,300)(223,304)(224,303)(225,307)
(226,306)(227,305)(228,309)(229,308)(230,312)(231,311)(232,310)(233,314)
(234,313)(235,317)(236,316)(237,315)(238,319)(239,318)(240,322)(241,321)
(242,320);
poly := sub<Sym(322)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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 >; 
 

to this polytope