Polytope of Type {2,8,10,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,10,4}*1280
if this polytope has a name.
Group : SmallGroup(1280,1044756)
Rank : 5
Schlafli Type : {2,8,10,4}
Number of vertices, edges, etc : 2, 8, 40, 20, 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 : {2,4,10,4}*640, {2,8,10,2}*640
4-fold quotients : {2,2,10,4}*320, {2,4,10,2}*320
5-fold quotients : {2,8,2,4}*256
8-fold quotients : {2,2,10,2}*160
10-fold quotients : {2,4,2,4}*128, {2,8,2,2}*128
16-fold quotients : {2,2,5,2}*80
20-fold quotients : {2,2,2,4}*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, 43)( 4, 44)( 5, 45)( 6, 46)( 7, 47)( 8, 48)( 9, 49)( 10, 50)
( 11, 51)( 12, 52)( 13, 53)( 14, 54)( 15, 55)( 16, 56)( 17, 57)( 18, 58)
( 19, 59)( 20, 60)( 21, 61)( 22, 62)( 23, 68)( 24, 69)( 25, 70)( 26, 71)
( 27, 72)( 28, 63)( 29, 64)( 30, 65)( 31, 66)( 32, 67)( 33, 78)( 34, 79)
( 35, 80)( 36, 81)( 37, 82)( 38, 73)( 39, 74)( 40, 75)( 41, 76)( 42, 77)
( 83,123)( 84,124)( 85,125)( 86,126)( 87,127)( 88,128)( 89,129)( 90,130)
( 91,131)( 92,132)( 93,133)( 94,134)( 95,135)( 96,136)( 97,137)( 98,138)
( 99,139)(100,140)(101,141)(102,142)(103,148)(104,149)(105,150)(106,151)
(107,152)(108,143)(109,144)(110,145)(111,146)(112,147)(113,158)(114,159)
(115,160)(116,161)(117,162)(118,153)(119,154)(120,155)(121,156)(122,157)
(163,203)(164,204)(165,205)(166,206)(167,207)(168,208)(169,209)(170,210)
(171,211)(172,212)(173,213)(174,214)(175,215)(176,216)(177,217)(178,218)
(179,219)(180,220)(181,221)(182,222)(183,228)(184,229)(185,230)(186,231)
(187,232)(188,223)(189,224)(190,225)(191,226)(192,227)(193,238)(194,239)
(195,240)(196,241)(197,242)(198,233)(199,234)(200,235)(201,236)(202,237)
(243,283)(244,284)(245,285)(246,286)(247,287)(248,288)(249,289)(250,290)
(251,291)(252,292)(253,293)(254,294)(255,295)(256,296)(257,297)(258,298)
(259,299)(260,300)(261,301)(262,302)(263,308)(264,309)(265,310)(266,311)
(267,312)(268,303)(269,304)(270,305)(271,306)(272,307)(273,318)(274,319)
(275,320)(276,321)(277,322)(278,313)(279,314)(280,315)(281,316)(282,317);;
s2 := ( 3,163)( 4,167)( 5,166)( 6,165)( 7,164)( 8,168)( 9,172)( 10,171)
( 11,170)( 12,169)( 13,173)( 14,177)( 15,176)( 16,175)( 17,174)( 18,178)
( 19,182)( 20,181)( 21,180)( 22,179)( 23,188)( 24,192)( 25,191)( 26,190)
( 27,189)( 28,183)( 29,187)( 30,186)( 31,185)( 32,184)( 33,198)( 34,202)
( 35,201)( 36,200)( 37,199)( 38,193)( 39,197)( 40,196)( 41,195)( 42,194)
( 43,223)( 44,227)( 45,226)( 46,225)( 47,224)( 48,228)( 49,232)( 50,231)
( 51,230)( 52,229)( 53,233)( 54,237)( 55,236)( 56,235)( 57,234)( 58,238)
( 59,242)( 60,241)( 61,240)( 62,239)( 63,203)( 64,207)( 65,206)( 66,205)
( 67,204)( 68,208)( 69,212)( 70,211)( 71,210)( 72,209)( 73,213)( 74,217)
( 75,216)( 76,215)( 77,214)( 78,218)( 79,222)( 80,221)( 81,220)( 82,219)
( 83,243)( 84,247)( 85,246)( 86,245)( 87,244)( 88,248)( 89,252)( 90,251)
( 91,250)( 92,249)( 93,253)( 94,257)( 95,256)( 96,255)( 97,254)( 98,258)
( 99,262)(100,261)(101,260)(102,259)(103,268)(104,272)(105,271)(106,270)
(107,269)(108,263)(109,267)(110,266)(111,265)(112,264)(113,278)(114,282)
(115,281)(116,280)(117,279)(118,273)(119,277)(120,276)(121,275)(122,274)
(123,303)(124,307)(125,306)(126,305)(127,304)(128,308)(129,312)(130,311)
(131,310)(132,309)(133,313)(134,317)(135,316)(136,315)(137,314)(138,318)
(139,322)(140,321)(141,320)(142,319)(143,283)(144,287)(145,286)(146,285)
(147,284)(148,288)(149,292)(150,291)(151,290)(152,289)(153,293)(154,297)
(155,296)(156,295)(157,294)(158,298)(159,302)(160,301)(161,300)(162,299);;
s3 := ( 3, 64)( 4, 63)( 5, 67)( 6, 66)( 7, 65)( 8, 69)( 9, 68)( 10, 72)
( 11, 71)( 12, 70)( 13, 74)( 14, 73)( 15, 77)( 16, 76)( 17, 75)( 18, 79)
( 19, 78)( 20, 82)( 21, 81)( 22, 80)( 23, 49)( 24, 48)( 25, 52)( 26, 51)
( 27, 50)( 28, 44)( 29, 43)( 30, 47)( 31, 46)( 32, 45)( 33, 59)( 34, 58)
( 35, 62)( 36, 61)( 37, 60)( 38, 54)( 39, 53)( 40, 57)( 41, 56)( 42, 55)
( 83,154)( 84,153)( 85,157)( 86,156)( 87,155)( 88,159)( 89,158)( 90,162)
( 91,161)( 92,160)( 93,144)( 94,143)( 95,147)( 96,146)( 97,145)( 98,149)
( 99,148)(100,152)(101,151)(102,150)(103,139)(104,138)(105,142)(106,141)
(107,140)(108,134)(109,133)(110,137)(111,136)(112,135)(113,129)(114,128)
(115,132)(116,131)(117,130)(118,124)(119,123)(120,127)(121,126)(122,125)
(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)
(243,294)(244,293)(245,297)(246,296)(247,295)(248,299)(249,298)(250,302)
(251,301)(252,300)(253,284)(254,283)(255,287)(256,286)(257,285)(258,289)
(259,288)(260,292)(261,291)(262,290)(263,314)(264,313)(265,317)(266,316)
(267,315)(268,319)(269,318)(270,322)(271,321)(272,320)(273,304)(274,303)
(275,307)(276,306)(277,305)(278,309)(279,308)(280,312)(281,311)(282,310);;
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, 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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(322)!(1,2);
s1 := Sym(322)!( 3, 43)( 4, 44)( 5, 45)( 6, 46)( 7, 47)( 8, 48)( 9, 49)
( 10, 50)( 11, 51)( 12, 52)( 13, 53)( 14, 54)( 15, 55)( 16, 56)( 17, 57)
( 18, 58)( 19, 59)( 20, 60)( 21, 61)( 22, 62)( 23, 68)( 24, 69)( 25, 70)
( 26, 71)( 27, 72)( 28, 63)( 29, 64)( 30, 65)( 31, 66)( 32, 67)( 33, 78)
( 34, 79)( 35, 80)( 36, 81)( 37, 82)( 38, 73)( 39, 74)( 40, 75)( 41, 76)
( 42, 77)( 83,123)( 84,124)( 85,125)( 86,126)( 87,127)( 88,128)( 89,129)
( 90,130)( 91,131)( 92,132)( 93,133)( 94,134)( 95,135)( 96,136)( 97,137)
( 98,138)( 99,139)(100,140)(101,141)(102,142)(103,148)(104,149)(105,150)
(106,151)(107,152)(108,143)(109,144)(110,145)(111,146)(112,147)(113,158)
(114,159)(115,160)(116,161)(117,162)(118,153)(119,154)(120,155)(121,156)
(122,157)(163,203)(164,204)(165,205)(166,206)(167,207)(168,208)(169,209)
(170,210)(171,211)(172,212)(173,213)(174,214)(175,215)(176,216)(177,217)
(178,218)(179,219)(180,220)(181,221)(182,222)(183,228)(184,229)(185,230)
(186,231)(187,232)(188,223)(189,224)(190,225)(191,226)(192,227)(193,238)
(194,239)(195,240)(196,241)(197,242)(198,233)(199,234)(200,235)(201,236)
(202,237)(243,283)(244,284)(245,285)(246,286)(247,287)(248,288)(249,289)
(250,290)(251,291)(252,292)(253,293)(254,294)(255,295)(256,296)(257,297)
(258,298)(259,299)(260,300)(261,301)(262,302)(263,308)(264,309)(265,310)
(266,311)(267,312)(268,303)(269,304)(270,305)(271,306)(272,307)(273,318)
(274,319)(275,320)(276,321)(277,322)(278,313)(279,314)(280,315)(281,316)
(282,317);
s2 := Sym(322)!( 3,163)( 4,167)( 5,166)( 6,165)( 7,164)( 8,168)( 9,172)
( 10,171)( 11,170)( 12,169)( 13,173)( 14,177)( 15,176)( 16,175)( 17,174)
( 18,178)( 19,182)( 20,181)( 21,180)( 22,179)( 23,188)( 24,192)( 25,191)
( 26,190)( 27,189)( 28,183)( 29,187)( 30,186)( 31,185)( 32,184)( 33,198)
( 34,202)( 35,201)( 36,200)( 37,199)( 38,193)( 39,197)( 40,196)( 41,195)
( 42,194)( 43,223)( 44,227)( 45,226)( 46,225)( 47,224)( 48,228)( 49,232)
( 50,231)( 51,230)( 52,229)( 53,233)( 54,237)( 55,236)( 56,235)( 57,234)
( 58,238)( 59,242)( 60,241)( 61,240)( 62,239)( 63,203)( 64,207)( 65,206)
( 66,205)( 67,204)( 68,208)( 69,212)( 70,211)( 71,210)( 72,209)( 73,213)
( 74,217)( 75,216)( 76,215)( 77,214)( 78,218)( 79,222)( 80,221)( 81,220)
( 82,219)( 83,243)( 84,247)( 85,246)( 86,245)( 87,244)( 88,248)( 89,252)
( 90,251)( 91,250)( 92,249)( 93,253)( 94,257)( 95,256)( 96,255)( 97,254)
( 98,258)( 99,262)(100,261)(101,260)(102,259)(103,268)(104,272)(105,271)
(106,270)(107,269)(108,263)(109,267)(110,266)(111,265)(112,264)(113,278)
(114,282)(115,281)(116,280)(117,279)(118,273)(119,277)(120,276)(121,275)
(122,274)(123,303)(124,307)(125,306)(126,305)(127,304)(128,308)(129,312)
(130,311)(131,310)(132,309)(133,313)(134,317)(135,316)(136,315)(137,314)
(138,318)(139,322)(140,321)(141,320)(142,319)(143,283)(144,287)(145,286)
(146,285)(147,284)(148,288)(149,292)(150,291)(151,290)(152,289)(153,293)
(154,297)(155,296)(156,295)(157,294)(158,298)(159,302)(160,301)(161,300)
(162,299);
s3 := Sym(322)!( 3, 64)( 4, 63)( 5, 67)( 6, 66)( 7, 65)( 8, 69)( 9, 68)
( 10, 72)( 11, 71)( 12, 70)( 13, 74)( 14, 73)( 15, 77)( 16, 76)( 17, 75)
( 18, 79)( 19, 78)( 20, 82)( 21, 81)( 22, 80)( 23, 49)( 24, 48)( 25, 52)
( 26, 51)( 27, 50)( 28, 44)( 29, 43)( 30, 47)( 31, 46)( 32, 45)( 33, 59)
( 34, 58)( 35, 62)( 36, 61)( 37, 60)( 38, 54)( 39, 53)( 40, 57)( 41, 56)
( 42, 55)( 83,154)( 84,153)( 85,157)( 86,156)( 87,155)( 88,159)( 89,158)
( 90,162)( 91,161)( 92,160)( 93,144)( 94,143)( 95,147)( 96,146)( 97,145)
( 98,149)( 99,148)(100,152)(101,151)(102,150)(103,139)(104,138)(105,142)
(106,141)(107,140)(108,134)(109,133)(110,137)(111,136)(112,135)(113,129)
(114,128)(115,132)(116,131)(117,130)(118,124)(119,123)(120,127)(121,126)
(122,125)(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)(243,294)(244,293)(245,297)(246,296)(247,295)(248,299)(249,298)
(250,302)(251,301)(252,300)(253,284)(254,283)(255,287)(256,286)(257,285)
(258,289)(259,288)(260,292)(261,291)(262,290)(263,314)(264,313)(265,317)
(266,316)(267,315)(268,319)(269,318)(270,322)(271,321)(272,320)(273,304)
(274,303)(275,307)(276,306)(277,305)(278,309)(279,308)(280,312)(281,311)
(282,310);
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,
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 >;
to this polytope