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Polytope of Type {2,10,8,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,8,4}*1280a
if this polytope has a name.
Group : SmallGroup(1280,1035859)
Rank : 5
Schlafli Type : {2,10,8,4}
Number of vertices, edges, etc : 2, 10, 40, 16, 4
Order of s0s1s2s3s4 : 40
Order of s0s1s2s3s4s3s2s1 : 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 : {2,10,4,4}*640, {2,10,8,2}*640
   4-fold quotients : {2,10,2,4}*320, {2,10,4,2}*320
   5-fold quotients : {2,2,8,4}*256a
   8-fold quotients : {2,5,2,4}*160, {2,10,2,2}*160
   10-fold quotients : {2,2,4,4}*128, {2,2,8,2}*128
   16-fold quotients : {2,5,2,2}*80
   20-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64
   40-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  3, 43)(  4, 47)(  5, 46)(  6, 45)(  7, 44)(  8, 48)(  9, 52)( 10, 51)
( 11, 50)( 12, 49)( 13, 53)( 14, 57)( 15, 56)( 16, 55)( 17, 54)( 18, 58)
( 19, 62)( 20, 61)( 21, 60)( 22, 59)( 23, 63)( 24, 67)( 25, 66)( 26, 65)
( 27, 64)( 28, 68)( 29, 72)( 30, 71)( 31, 70)( 32, 69)( 33, 73)( 34, 77)
( 35, 76)( 36, 75)( 37, 74)( 38, 78)( 39, 82)( 40, 81)( 41, 80)( 42, 79)
( 83,123)( 84,127)( 85,126)( 86,125)( 87,124)( 88,128)( 89,132)( 90,131)
( 91,130)( 92,129)( 93,133)( 94,137)( 95,136)( 96,135)( 97,134)( 98,138)
( 99,142)(100,141)(101,140)(102,139)(103,143)(104,147)(105,146)(106,145)
(107,144)(108,148)(109,152)(110,151)(111,150)(112,149)(113,153)(114,157)
(115,156)(116,155)(117,154)(118,158)(119,162)(120,161)(121,160)(122,159)
(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)(183,223)(184,227)(185,226)(186,225)
(187,224)(188,228)(189,232)(190,231)(191,230)(192,229)(193,233)(194,237)
(195,236)(196,235)(197,234)(198,238)(199,242)(200,241)(201,240)(202,239)
(243,283)(244,287)(245,286)(246,285)(247,284)(248,288)(249,292)(250,291)
(251,290)(252,289)(253,293)(254,297)(255,296)(256,295)(257,294)(258,298)
(259,302)(260,301)(261,300)(262,299)(263,303)(264,307)(265,306)(266,305)
(267,304)(268,308)(269,312)(270,311)(271,310)(272,309)(273,313)(274,317)
(275,316)(276,315)(277,314)(278,318)(279,322)(280,321)(281,320)(282,319);;
s2 := (  3,204)(  4,203)(  5,207)(  6,206)(  7,205)(  8,209)(  9,208)( 10,212)
( 11,211)( 12,210)( 13,214)( 14,213)( 15,217)( 16,216)( 17,215)( 18,219)
( 19,218)( 20,222)( 21,221)( 22,220)( 23,229)( 24,228)( 25,232)( 26,231)
( 27,230)( 28,224)( 29,223)( 30,227)( 31,226)( 32,225)( 33,239)( 34,238)
( 35,242)( 36,241)( 37,240)( 38,234)( 39,233)( 40,237)( 41,236)( 42,235)
( 43,164)( 44,163)( 45,167)( 46,166)( 47,165)( 48,169)( 49,168)( 50,172)
( 51,171)( 52,170)( 53,174)( 54,173)( 55,177)( 56,176)( 57,175)( 58,179)
( 59,178)( 60,182)( 61,181)( 62,180)( 63,189)( 64,188)( 65,192)( 66,191)
( 67,190)( 68,184)( 69,183)( 70,187)( 71,186)( 72,185)( 73,199)( 74,198)
( 75,202)( 76,201)( 77,200)( 78,194)( 79,193)( 80,197)( 81,196)( 82,195)
( 83,284)( 84,283)( 85,287)( 86,286)( 87,285)( 88,289)( 89,288)( 90,292)
( 91,291)( 92,290)( 93,294)( 94,293)( 95,297)( 96,296)( 97,295)( 98,299)
( 99,298)(100,302)(101,301)(102,300)(103,309)(104,308)(105,312)(106,311)
(107,310)(108,304)(109,303)(110,307)(111,306)(112,305)(113,319)(114,318)
(115,322)(116,321)(117,320)(118,314)(119,313)(120,317)(121,316)(122,315)
(123,244)(124,243)(125,247)(126,246)(127,245)(128,249)(129,248)(130,252)
(131,251)(132,250)(133,254)(134,253)(135,257)(136,256)(137,255)(138,259)
(139,258)(140,262)(141,261)(142,260)(143,269)(144,268)(145,272)(146,271)
(147,270)(148,264)(149,263)(150,267)(151,266)(152,265)(153,279)(154,278)
(155,282)(156,281)(157,280)(158,274)(159,273)(160,277)(161,276)(162,275);;
s3 := ( 23, 28)( 24, 29)( 25, 30)( 26, 31)( 27, 32)( 33, 38)( 34, 39)( 35, 40)
( 36, 41)( 37, 42)( 63, 68)( 64, 69)( 65, 70)( 66, 71)( 67, 72)( 73, 78)
( 74, 79)( 75, 80)( 76, 81)( 77, 82)( 83, 93)( 84, 94)( 85, 95)( 86, 96)
( 87, 97)( 88, 98)( 89, 99)( 90,100)( 91,101)( 92,102)(103,118)(104,119)
(105,120)(106,121)(107,122)(108,113)(109,114)(110,115)(111,116)(112,117)
(123,133)(124,134)(125,135)(126,136)(127,137)(128,138)(129,139)(130,140)
(131,141)(132,142)(143,158)(144,159)(145,160)(146,161)(147,162)(148,153)
(149,154)(150,155)(151,156)(152,157)(163,183)(164,184)(165,185)(166,186)
(167,187)(168,188)(169,189)(170,190)(171,191)(172,192)(173,193)(174,194)
(175,195)(176,196)(177,197)(178,198)(179,199)(180,200)(181,201)(182,202)
(203,223)(204,224)(205,225)(206,226)(207,227)(208,228)(209,229)(210,230)
(211,231)(212,232)(213,233)(214,234)(215,235)(216,236)(217,237)(218,238)
(219,239)(220,240)(221,241)(222,242)(243,273)(244,274)(245,275)(246,276)
(247,277)(248,278)(249,279)(250,280)(251,281)(252,282)(253,263)(254,264)
(255,265)(256,266)(257,267)(258,268)(259,269)(260,270)(261,271)(262,272)
(283,313)(284,314)(285,315)(286,316)(287,317)(288,318)(289,319)(290,320)
(291,321)(292,322)(293,303)(294,304)(295,305)(296,306)(297,307)(298,308)
(299,309)(300,310)(301,311)(302,312);;
s4 := (  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)( 23,103)( 24,104)( 25,105)( 26,106)
( 27,107)( 28,108)( 29,109)( 30,110)( 31,111)( 32,112)( 33,113)( 34,114)
( 35,115)( 36,116)( 37,117)( 38,118)( 39,119)( 40,120)( 41,121)( 42,122)
( 43,123)( 44,124)( 45,125)( 46,126)( 47,127)( 48,128)( 49,129)( 50,130)
( 51,131)( 52,132)( 53,133)( 54,134)( 55,135)( 56,136)( 57,137)( 58,138)
( 59,139)( 60,140)( 61,141)( 62,142)( 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)(183,263)(184,264)(185,265)(186,266)
(187,267)(188,268)(189,269)(190,270)(191,271)(192,272)(193,273)(194,274)
(195,275)(196,276)(197,277)(198,278)(199,279)(200,280)(201,281)(202,282)
(203,283)(204,284)(205,285)(206,286)(207,287)(208,288)(209,289)(210,290)
(211,291)(212,292)(213,293)(214,294)(215,295)(216,296)(217,297)(218,298)
(219,299)(220,300)(221,301)(222,302)(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);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, 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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(322)!(1,2);
s1 := Sym(322)!(  3, 43)(  4, 47)(  5, 46)(  6, 45)(  7, 44)(  8, 48)(  9, 52)
( 10, 51)( 11, 50)( 12, 49)( 13, 53)( 14, 57)( 15, 56)( 16, 55)( 17, 54)
( 18, 58)( 19, 62)( 20, 61)( 21, 60)( 22, 59)( 23, 63)( 24, 67)( 25, 66)
( 26, 65)( 27, 64)( 28, 68)( 29, 72)( 30, 71)( 31, 70)( 32, 69)( 33, 73)
( 34, 77)( 35, 76)( 36, 75)( 37, 74)( 38, 78)( 39, 82)( 40, 81)( 41, 80)
( 42, 79)( 83,123)( 84,127)( 85,126)( 86,125)( 87,124)( 88,128)( 89,132)
( 90,131)( 91,130)( 92,129)( 93,133)( 94,137)( 95,136)( 96,135)( 97,134)
( 98,138)( 99,142)(100,141)(101,140)(102,139)(103,143)(104,147)(105,146)
(106,145)(107,144)(108,148)(109,152)(110,151)(111,150)(112,149)(113,153)
(114,157)(115,156)(116,155)(117,154)(118,158)(119,162)(120,161)(121,160)
(122,159)(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)(183,223)(184,227)(185,226)
(186,225)(187,224)(188,228)(189,232)(190,231)(191,230)(192,229)(193,233)
(194,237)(195,236)(196,235)(197,234)(198,238)(199,242)(200,241)(201,240)
(202,239)(243,283)(244,287)(245,286)(246,285)(247,284)(248,288)(249,292)
(250,291)(251,290)(252,289)(253,293)(254,297)(255,296)(256,295)(257,294)
(258,298)(259,302)(260,301)(261,300)(262,299)(263,303)(264,307)(265,306)
(266,305)(267,304)(268,308)(269,312)(270,311)(271,310)(272,309)(273,313)
(274,317)(275,316)(276,315)(277,314)(278,318)(279,322)(280,321)(281,320)
(282,319);
s2 := Sym(322)!(  3,204)(  4,203)(  5,207)(  6,206)(  7,205)(  8,209)(  9,208)
( 10,212)( 11,211)( 12,210)( 13,214)( 14,213)( 15,217)( 16,216)( 17,215)
( 18,219)( 19,218)( 20,222)( 21,221)( 22,220)( 23,229)( 24,228)( 25,232)
( 26,231)( 27,230)( 28,224)( 29,223)( 30,227)( 31,226)( 32,225)( 33,239)
( 34,238)( 35,242)( 36,241)( 37,240)( 38,234)( 39,233)( 40,237)( 41,236)
( 42,235)( 43,164)( 44,163)( 45,167)( 46,166)( 47,165)( 48,169)( 49,168)
( 50,172)( 51,171)( 52,170)( 53,174)( 54,173)( 55,177)( 56,176)( 57,175)
( 58,179)( 59,178)( 60,182)( 61,181)( 62,180)( 63,189)( 64,188)( 65,192)
( 66,191)( 67,190)( 68,184)( 69,183)( 70,187)( 71,186)( 72,185)( 73,199)
( 74,198)( 75,202)( 76,201)( 77,200)( 78,194)( 79,193)( 80,197)( 81,196)
( 82,195)( 83,284)( 84,283)( 85,287)( 86,286)( 87,285)( 88,289)( 89,288)
( 90,292)( 91,291)( 92,290)( 93,294)( 94,293)( 95,297)( 96,296)( 97,295)
( 98,299)( 99,298)(100,302)(101,301)(102,300)(103,309)(104,308)(105,312)
(106,311)(107,310)(108,304)(109,303)(110,307)(111,306)(112,305)(113,319)
(114,318)(115,322)(116,321)(117,320)(118,314)(119,313)(120,317)(121,316)
(122,315)(123,244)(124,243)(125,247)(126,246)(127,245)(128,249)(129,248)
(130,252)(131,251)(132,250)(133,254)(134,253)(135,257)(136,256)(137,255)
(138,259)(139,258)(140,262)(141,261)(142,260)(143,269)(144,268)(145,272)
(146,271)(147,270)(148,264)(149,263)(150,267)(151,266)(152,265)(153,279)
(154,278)(155,282)(156,281)(157,280)(158,274)(159,273)(160,277)(161,276)
(162,275);
s3 := Sym(322)!( 23, 28)( 24, 29)( 25, 30)( 26, 31)( 27, 32)( 33, 38)( 34, 39)
( 35, 40)( 36, 41)( 37, 42)( 63, 68)( 64, 69)( 65, 70)( 66, 71)( 67, 72)
( 73, 78)( 74, 79)( 75, 80)( 76, 81)( 77, 82)( 83, 93)( 84, 94)( 85, 95)
( 86, 96)( 87, 97)( 88, 98)( 89, 99)( 90,100)( 91,101)( 92,102)(103,118)
(104,119)(105,120)(106,121)(107,122)(108,113)(109,114)(110,115)(111,116)
(112,117)(123,133)(124,134)(125,135)(126,136)(127,137)(128,138)(129,139)
(130,140)(131,141)(132,142)(143,158)(144,159)(145,160)(146,161)(147,162)
(148,153)(149,154)(150,155)(151,156)(152,157)(163,183)(164,184)(165,185)
(166,186)(167,187)(168,188)(169,189)(170,190)(171,191)(172,192)(173,193)
(174,194)(175,195)(176,196)(177,197)(178,198)(179,199)(180,200)(181,201)
(182,202)(203,223)(204,224)(205,225)(206,226)(207,227)(208,228)(209,229)
(210,230)(211,231)(212,232)(213,233)(214,234)(215,235)(216,236)(217,237)
(218,238)(219,239)(220,240)(221,241)(222,242)(243,273)(244,274)(245,275)
(246,276)(247,277)(248,278)(249,279)(250,280)(251,281)(252,282)(253,263)
(254,264)(255,265)(256,266)(257,267)(258,268)(259,269)(260,270)(261,271)
(262,272)(283,313)(284,314)(285,315)(286,316)(287,317)(288,318)(289,319)
(290,320)(291,321)(292,322)(293,303)(294,304)(295,305)(296,306)(297,307)
(298,308)(299,309)(300,310)(301,311)(302,312);
s4 := 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)( 23,103)( 24,104)( 25,105)
( 26,106)( 27,107)( 28,108)( 29,109)( 30,110)( 31,111)( 32,112)( 33,113)
( 34,114)( 35,115)( 36,116)( 37,117)( 38,118)( 39,119)( 40,120)( 41,121)
( 42,122)( 43,123)( 44,124)( 45,125)( 46,126)( 47,127)( 48,128)( 49,129)
( 50,130)( 51,131)( 52,132)( 53,133)( 54,134)( 55,135)( 56,136)( 57,137)
( 58,138)( 59,139)( 60,140)( 61,141)( 62,142)( 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)(183,263)(184,264)(185,265)
(186,266)(187,267)(188,268)(189,269)(190,270)(191,271)(192,272)(193,273)
(194,274)(195,275)(196,276)(197,277)(198,278)(199,279)(200,280)(201,281)
(202,282)(203,283)(204,284)(205,285)(206,286)(207,287)(208,288)(209,289)
(210,290)(211,291)(212,292)(213,293)(214,294)(215,295)(216,296)(217,297)
(218,298)(219,299)(220,300)(221,301)(222,302)(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);
poly := sub<Sym(322)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
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 >; 
 

to this polytope