Polytope of Type {2,8,40}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,40}*1280c
if this polytope has a name.
Group : SmallGroup(1280,145174)
Rank : 4
Schlafli Type : {2,8,40}
Number of vertices, edges, etc : 2, 8, 160, 40
Order of s₀s₁s₂s₃ : 40
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 : {2,4,40}*640a, {2,8,20}*640a
   4-fold quotients : {2,4,20}*320, {2,2,40}*320, {2,8,10}*320
   5-fold quotients : {2,8,8}*256b
   8-fold quotients : {2,2,20}*160, {2,4,10}*160
   10-fold quotients : {2,4,8}*128a, {2,8,4}*128a
   16-fold quotients : {2,2,10}*80
   20-fold quotients : {2,4,4}*64, {2,2,8}*64, {2,8,2}*64
   32-fold quotients : {2,2,5}*40
   40-fold quotients : {2,2,4}*32, {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 := (  3, 83)(  4, 84)(  5, 85)(  6, 86)(  7, 87)(  8, 88)(  9, 89)( 10, 90)
( 11, 91)( 12, 92)( 13, 93)( 14, 94)( 15, 95)( 16, 96)( 17, 97)( 18, 98)
( 19, 99)( 20,100)( 21,101)( 22,102)( 23,108)( 24,109)( 25,110)( 26,111)
( 27,112)( 28,103)( 29,104)( 30,105)( 31,106)( 32,107)( 33,118)( 34,119)
( 35,120)( 36,121)( 37,122)( 38,113)( 39,114)( 40,115)( 41,116)( 42,117)
( 43,128)( 44,129)( 45,130)( 46,131)( 47,132)( 48,123)( 49,124)( 50,125)
( 51,126)( 52,127)( 53,138)( 54,139)( 55,140)( 56,141)( 57,142)( 58,133)
( 59,134)( 60,135)( 61,136)( 62,137)( 63,143)( 64,144)( 65,145)( 66,146)
( 67,147)( 68,148)( 69,149)( 70,150)( 71,151)( 72,152)( 73,153)( 74,154)
( 75,155)( 76,156)( 77,157)( 78,158)( 79,159)( 80,160)( 81,161)( 82,162)
(163,243)(164,244)(165,245)(166,246)(167,247)(168,248)(169,249)(170,250)
(171,251)(172,252)(173,253)(174,254)(175,255)(176,256)(177,257)(178,258)
(179,259)(180,260)(181,261)(182,262)(183,268)(184,269)(185,270)(186,271)
(187,272)(188,263)(189,264)(190,265)(191,266)(192,267)(193,278)(194,279)
(195,280)(196,281)(197,282)(198,273)(199,274)(200,275)(201,276)(202,277)
(203,288)(204,289)(205,290)(206,291)(207,292)(208,283)(209,284)(210,285)
(211,286)(212,287)(213,298)(214,299)(215,300)(216,301)(217,302)(218,293)
(219,294)(220,295)(221,296)(222,297)(223,303)(224,304)(225,305)(226,306)
(227,307)(228,308)(229,309)(230,310)(231,311)(232,312)(233,313)(234,314)
(235,315)(236,316)(237,317)(238,318)(239,319)(240,320)(241,321)(242,322);;
s2 := (  4,  7)(  5,  6)(  9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)( 20, 21)
( 23, 28)( 24, 32)( 25, 31)( 26, 30)( 27, 29)( 33, 38)( 34, 42)( 35, 41)
( 36, 40)( 37, 39)( 43, 53)( 44, 57)( 45, 56)( 46, 55)( 47, 54)( 48, 58)
( 49, 62)( 50, 61)( 51, 60)( 52, 59)( 63, 78)( 64, 82)( 65, 81)( 66, 80)
( 67, 79)( 68, 73)( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 83,103)( 84,107)
( 85,106)( 86,105)( 87,104)( 88,108)( 89,112)( 90,111)( 91,110)( 92,109)
( 93,113)( 94,117)( 95,116)( 96,115)( 97,114)( 98,118)( 99,122)(100,121)
(101,120)(102,119)(123,153)(124,157)(125,156)(126,155)(127,154)(128,158)
(129,162)(130,161)(131,160)(132,159)(133,143)(134,147)(135,146)(136,145)
(137,144)(138,148)(139,152)(140,151)(141,150)(142,149)(163,203)(164,207)
(165,206)(166,205)(167,204)(168,208)(169,212)(170,211)(171,210)(172,209)
(173,213)(174,217)(175,216)(176,215)(177,214)(178,218)(179,222)(180,221)
(181,220)(182,219)(183,228)(184,232)(185,231)(186,230)(187,229)(188,223)
(189,227)(190,226)(191,225)(192,224)(193,238)(194,242)(195,241)(196,240)
(197,239)(198,233)(199,237)(200,236)(201,235)(202,234)(243,308)(244,312)
(245,311)(246,310)(247,309)(248,303)(249,307)(250,306)(251,305)(252,304)
(253,318)(254,322)(255,321)(256,320)(257,319)(258,313)(259,317)(260,316)
(261,315)(262,314)(263,288)(264,292)(265,291)(266,290)(267,289)(268,283)
(269,287)(270,286)(271,285)(272,284)(273,298)(274,302)(275,301)(276,300)
(277,299)(278,293)(279,297)(280,296)(281,295)(282,294);;
s3 := (  3,244)(  4,243)(  5,247)(  6,246)(  7,245)(  8,249)(  9,248)( 10,252)
( 11,251)( 12,250)( 13,254)( 14,253)( 15,257)( 16,256)( 17,255)( 18,259)
( 19,258)( 20,262)( 21,261)( 22,260)( 23,264)( 24,263)( 25,267)( 26,266)
( 27,265)( 28,269)( 29,268)( 30,272)( 31,271)( 32,270)( 33,274)( 34,273)
( 35,277)( 36,276)( 37,275)( 38,279)( 39,278)( 40,282)( 41,281)( 42,280)
( 43,299)( 44,298)( 45,302)( 46,301)( 47,300)( 48,294)( 49,293)( 50,297)
( 51,296)( 52,295)( 53,289)( 54,288)( 55,292)( 56,291)( 57,290)( 58,284)
( 59,283)( 60,287)( 61,286)( 62,285)( 63,319)( 64,318)( 65,322)( 66,321)
( 67,320)( 68,314)( 69,313)( 70,317)( 71,316)( 72,315)( 73,309)( 74,308)
( 75,312)( 76,311)( 77,310)( 78,304)( 79,303)( 80,307)( 81,306)( 82,305)
( 83,164)( 84,163)( 85,167)( 86,166)( 87,165)( 88,169)( 89,168)( 90,172)
( 91,171)( 92,170)( 93,174)( 94,173)( 95,177)( 96,176)( 97,175)( 98,179)
( 99,178)(100,182)(101,181)(102,180)(103,184)(104,183)(105,187)(106,186)
(107,185)(108,189)(109,188)(110,192)(111,191)(112,190)(113,194)(114,193)
(115,197)(116,196)(117,195)(118,199)(119,198)(120,202)(121,201)(122,200)
(123,219)(124,218)(125,222)(126,221)(127,220)(128,214)(129,213)(130,217)
(131,216)(132,215)(133,209)(134,208)(135,212)(136,211)(137,210)(138,204)
(139,203)(140,207)(141,206)(142,205)(143,239)(144,238)(145,242)(146,241)
(147,240)(148,234)(149,233)(150,237)(151,236)(152,235)(153,229)(154,228)
(155,232)(156,231)(157,230)(158,224)(159,223)(160,227)(161,226)(162,225);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(322)!(1,2);
s1 := Sym(322)!(  3, 83)(  4, 84)(  5, 85)(  6, 86)(  7, 87)(  8, 88)(  9, 89)
( 10, 90)( 11, 91)( 12, 92)( 13, 93)( 14, 94)( 15, 95)( 16, 96)( 17, 97)
( 18, 98)( 19, 99)( 20,100)( 21,101)( 22,102)( 23,108)( 24,109)( 25,110)
( 26,111)( 27,112)( 28,103)( 29,104)( 30,105)( 31,106)( 32,107)( 33,118)
( 34,119)( 35,120)( 36,121)( 37,122)( 38,113)( 39,114)( 40,115)( 41,116)
( 42,117)( 43,128)( 44,129)( 45,130)( 46,131)( 47,132)( 48,123)( 49,124)
( 50,125)( 51,126)( 52,127)( 53,138)( 54,139)( 55,140)( 56,141)( 57,142)
( 58,133)( 59,134)( 60,135)( 61,136)( 62,137)( 63,143)( 64,144)( 65,145)
( 66,146)( 67,147)( 68,148)( 69,149)( 70,150)( 71,151)( 72,152)( 73,153)
( 74,154)( 75,155)( 76,156)( 77,157)( 78,158)( 79,159)( 80,160)( 81,161)
( 82,162)(163,243)(164,244)(165,245)(166,246)(167,247)(168,248)(169,249)
(170,250)(171,251)(172,252)(173,253)(174,254)(175,255)(176,256)(177,257)
(178,258)(179,259)(180,260)(181,261)(182,262)(183,268)(184,269)(185,270)
(186,271)(187,272)(188,263)(189,264)(190,265)(191,266)(192,267)(193,278)
(194,279)(195,280)(196,281)(197,282)(198,273)(199,274)(200,275)(201,276)
(202,277)(203,288)(204,289)(205,290)(206,291)(207,292)(208,283)(209,284)
(210,285)(211,286)(212,287)(213,298)(214,299)(215,300)(216,301)(217,302)
(218,293)(219,294)(220,295)(221,296)(222,297)(223,303)(224,304)(225,305)
(226,306)(227,307)(228,308)(229,309)(230,310)(231,311)(232,312)(233,313)
(234,314)(235,315)(236,316)(237,317)(238,318)(239,319)(240,320)(241,321)
(242,322);
s2 := Sym(322)!(  4,  7)(  5,  6)(  9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)
( 20, 21)( 23, 28)( 24, 32)( 25, 31)( 26, 30)( 27, 29)( 33, 38)( 34, 42)
( 35, 41)( 36, 40)( 37, 39)( 43, 53)( 44, 57)( 45, 56)( 46, 55)( 47, 54)
( 48, 58)( 49, 62)( 50, 61)( 51, 60)( 52, 59)( 63, 78)( 64, 82)( 65, 81)
( 66, 80)( 67, 79)( 68, 73)( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 83,103)
( 84,107)( 85,106)( 86,105)( 87,104)( 88,108)( 89,112)( 90,111)( 91,110)
( 92,109)( 93,113)( 94,117)( 95,116)( 96,115)( 97,114)( 98,118)( 99,122)
(100,121)(101,120)(102,119)(123,153)(124,157)(125,156)(126,155)(127,154)
(128,158)(129,162)(130,161)(131,160)(132,159)(133,143)(134,147)(135,146)
(136,145)(137,144)(138,148)(139,152)(140,151)(141,150)(142,149)(163,203)
(164,207)(165,206)(166,205)(167,204)(168,208)(169,212)(170,211)(171,210)
(172,209)(173,213)(174,217)(175,216)(176,215)(177,214)(178,218)(179,222)
(180,221)(181,220)(182,219)(183,228)(184,232)(185,231)(186,230)(187,229)
(188,223)(189,227)(190,226)(191,225)(192,224)(193,238)(194,242)(195,241)
(196,240)(197,239)(198,233)(199,237)(200,236)(201,235)(202,234)(243,308)
(244,312)(245,311)(246,310)(247,309)(248,303)(249,307)(250,306)(251,305)
(252,304)(253,318)(254,322)(255,321)(256,320)(257,319)(258,313)(259,317)
(260,316)(261,315)(262,314)(263,288)(264,292)(265,291)(266,290)(267,289)
(268,283)(269,287)(270,286)(271,285)(272,284)(273,298)(274,302)(275,301)
(276,300)(277,299)(278,293)(279,297)(280,296)(281,295)(282,294);
s3 := Sym(322)!(  3,244)(  4,243)(  5,247)(  6,246)(  7,245)(  8,249)(  9,248)
( 10,252)( 11,251)( 12,250)( 13,254)( 14,253)( 15,257)( 16,256)( 17,255)
( 18,259)( 19,258)( 20,262)( 21,261)( 22,260)( 23,264)( 24,263)( 25,267)
( 26,266)( 27,265)( 28,269)( 29,268)( 30,272)( 31,271)( 32,270)( 33,274)
( 34,273)( 35,277)( 36,276)( 37,275)( 38,279)( 39,278)( 40,282)( 41,281)
( 42,280)( 43,299)( 44,298)( 45,302)( 46,301)( 47,300)( 48,294)( 49,293)
( 50,297)( 51,296)( 52,295)( 53,289)( 54,288)( 55,292)( 56,291)( 57,290)
( 58,284)( 59,283)( 60,287)( 61,286)( 62,285)( 63,319)( 64,318)( 65,322)
( 66,321)( 67,320)( 68,314)( 69,313)( 70,317)( 71,316)( 72,315)( 73,309)
( 74,308)( 75,312)( 76,311)( 77,310)( 78,304)( 79,303)( 80,307)( 81,306)
( 82,305)( 83,164)( 84,163)( 85,167)( 86,166)( 87,165)( 88,169)( 89,168)
( 90,172)( 91,171)( 92,170)( 93,174)( 94,173)( 95,177)( 96,176)( 97,175)
( 98,179)( 99,178)(100,182)(101,181)(102,180)(103,184)(104,183)(105,187)
(106,186)(107,185)(108,189)(109,188)(110,192)(111,191)(112,190)(113,194)
(114,193)(115,197)(116,196)(117,195)(118,199)(119,198)(120,202)(121,201)
(122,200)(123,219)(124,218)(125,222)(126,221)(127,220)(128,214)(129,213)
(130,217)(131,216)(132,215)(133,209)(134,208)(135,212)(136,211)(137,210)
(138,204)(139,203)(140,207)(141,206)(142,205)(143,239)(144,238)(145,242)
(146,241)(147,240)(148,234)(149,233)(150,237)(151,236)(152,235)(153,229)
(154,228)(155,232)(156,231)(157,230)(158,224)(159,223)(160,227)(161,226)
(162,225);
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope