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

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

to this polytope