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

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

to this polytope