Polytope of Type {2,4,10,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,10,8}*1280
if this polytope has a name.
Group : SmallGroup(1280,1044756)
Rank : 5
Schlafli Type : {2,4,10,8}
Number of vertices, edges, etc : 2, 4, 20, 40, 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 : {2,4,10,4}*640, {2,2,10,8}*640
4-fold quotients : {2,2,10,4}*320, {2,4,10,2}*320
5-fold quotients : {2,4,2,8}*256
8-fold quotients : {2,2,10,2}*160
10-fold quotients : {2,4,2,4}*128, {2,2,2,8}*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, 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);;
s2 := ( 3, 63)( 4, 67)( 5, 66)( 6, 65)( 7, 64)( 8, 68)( 9, 72)( 10, 71)
( 11, 70)( 12, 69)( 13, 73)( 14, 77)( 15, 76)( 16, 75)( 17, 74)( 18, 78)
( 19, 82)( 20, 81)( 21, 80)( 22, 79)( 23, 48)( 24, 52)( 25, 51)( 26, 50)
( 27, 49)( 28, 43)( 29, 47)( 30, 46)( 31, 45)( 32, 44)( 33, 58)( 34, 62)
( 35, 61)( 36, 60)( 37, 59)( 38, 53)( 39, 57)( 40, 56)( 41, 55)( 42, 54)
( 83,153)( 84,157)( 85,156)( 86,155)( 87,154)( 88,158)( 89,162)( 90,161)
( 91,160)( 92,159)( 93,143)( 94,147)( 95,146)( 96,145)( 97,144)( 98,148)
( 99,152)(100,151)(101,150)(102,149)(103,138)(104,142)(105,141)(106,140)
(107,139)(108,133)(109,137)(110,136)(111,135)(112,134)(113,128)(114,132)
(115,131)(116,130)(117,129)(118,123)(119,127)(120,126)(121,125)(122,124)
(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)
(243,293)(244,297)(245,296)(246,295)(247,294)(248,298)(249,302)(250,301)
(251,300)(252,299)(253,283)(254,287)(255,286)(256,285)(257,284)(258,288)
(259,292)(260,291)(261,290)(262,289)(263,313)(264,317)(265,316)(266,315)
(267,314)(268,318)(269,322)(270,321)(271,320)(272,319)(273,303)(274,307)
(275,306)(276,305)(277,304)(278,308)(279,312)(280,311)(281,310)(282,309);;
s3 := ( 3,164)( 4,163)( 5,167)( 6,166)( 7,165)( 8,169)( 9,168)( 10,172)
( 11,171)( 12,170)( 13,174)( 14,173)( 15,177)( 16,176)( 17,175)( 18,179)
( 19,178)( 20,182)( 21,181)( 22,180)( 23,189)( 24,188)( 25,192)( 26,191)
( 27,190)( 28,184)( 29,183)( 30,187)( 31,186)( 32,185)( 33,199)( 34,198)
( 35,202)( 36,201)( 37,200)( 38,194)( 39,193)( 40,197)( 41,196)( 42,195)
( 43,224)( 44,223)( 45,227)( 46,226)( 47,225)( 48,229)( 49,228)( 50,232)
( 51,231)( 52,230)( 53,234)( 54,233)( 55,237)( 56,236)( 57,235)( 58,239)
( 59,238)( 60,242)( 61,241)( 62,240)( 63,204)( 64,203)( 65,207)( 66,206)
( 67,205)( 68,209)( 69,208)( 70,212)( 71,211)( 72,210)( 73,214)( 74,213)
( 75,217)( 76,216)( 77,215)( 78,219)( 79,218)( 80,222)( 81,221)( 82,220)
( 83,244)( 84,243)( 85,247)( 86,246)( 87,245)( 88,249)( 89,248)( 90,252)
( 91,251)( 92,250)( 93,254)( 94,253)( 95,257)( 96,256)( 97,255)( 98,259)
( 99,258)(100,262)(101,261)(102,260)(103,269)(104,268)(105,272)(106,271)
(107,270)(108,264)(109,263)(110,267)(111,266)(112,265)(113,279)(114,278)
(115,282)(116,281)(117,280)(118,274)(119,273)(120,277)(121,276)(122,275)
(123,304)(124,303)(125,307)(126,306)(127,305)(128,309)(129,308)(130,312)
(131,311)(132,310)(133,314)(134,313)(135,317)(136,316)(137,315)(138,319)
(139,318)(140,322)(141,321)(142,320)(143,284)(144,283)(145,287)(146,286)
(147,285)(148,289)(149,288)(150,292)(151,291)(152,290)(153,294)(154,293)
(155,297)(156,296)(157,295)(158,299)(159,298)(160,302)(161,301)(162,300);;
s4 := ( 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);;
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*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
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)( 23,103)( 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);
s2 := Sym(322)!( 3, 63)( 4, 67)( 5, 66)( 6, 65)( 7, 64)( 8, 68)( 9, 72)
( 10, 71)( 11, 70)( 12, 69)( 13, 73)( 14, 77)( 15, 76)( 16, 75)( 17, 74)
( 18, 78)( 19, 82)( 20, 81)( 21, 80)( 22, 79)( 23, 48)( 24, 52)( 25, 51)
( 26, 50)( 27, 49)( 28, 43)( 29, 47)( 30, 46)( 31, 45)( 32, 44)( 33, 58)
( 34, 62)( 35, 61)( 36, 60)( 37, 59)( 38, 53)( 39, 57)( 40, 56)( 41, 55)
( 42, 54)( 83,153)( 84,157)( 85,156)( 86,155)( 87,154)( 88,158)( 89,162)
( 90,161)( 91,160)( 92,159)( 93,143)( 94,147)( 95,146)( 96,145)( 97,144)
( 98,148)( 99,152)(100,151)(101,150)(102,149)(103,138)(104,142)(105,141)
(106,140)(107,139)(108,133)(109,137)(110,136)(111,135)(112,134)(113,128)
(114,132)(115,131)(116,130)(117,129)(118,123)(119,127)(120,126)(121,125)
(122,124)(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)(243,293)(244,297)(245,296)(246,295)(247,294)(248,298)(249,302)
(250,301)(251,300)(252,299)(253,283)(254,287)(255,286)(256,285)(257,284)
(258,288)(259,292)(260,291)(261,290)(262,289)(263,313)(264,317)(265,316)
(266,315)(267,314)(268,318)(269,322)(270,321)(271,320)(272,319)(273,303)
(274,307)(275,306)(276,305)(277,304)(278,308)(279,312)(280,311)(281,310)
(282,309);
s3 := Sym(322)!( 3,164)( 4,163)( 5,167)( 6,166)( 7,165)( 8,169)( 9,168)
( 10,172)( 11,171)( 12,170)( 13,174)( 14,173)( 15,177)( 16,176)( 17,175)
( 18,179)( 19,178)( 20,182)( 21,181)( 22,180)( 23,189)( 24,188)( 25,192)
( 26,191)( 27,190)( 28,184)( 29,183)( 30,187)( 31,186)( 32,185)( 33,199)
( 34,198)( 35,202)( 36,201)( 37,200)( 38,194)( 39,193)( 40,197)( 41,196)
( 42,195)( 43,224)( 44,223)( 45,227)( 46,226)( 47,225)( 48,229)( 49,228)
( 50,232)( 51,231)( 52,230)( 53,234)( 54,233)( 55,237)( 56,236)( 57,235)
( 58,239)( 59,238)( 60,242)( 61,241)( 62,240)( 63,204)( 64,203)( 65,207)
( 66,206)( 67,205)( 68,209)( 69,208)( 70,212)( 71,211)( 72,210)( 73,214)
( 74,213)( 75,217)( 76,216)( 77,215)( 78,219)( 79,218)( 80,222)( 81,221)
( 82,220)( 83,244)( 84,243)( 85,247)( 86,246)( 87,245)( 88,249)( 89,248)
( 90,252)( 91,251)( 92,250)( 93,254)( 94,253)( 95,257)( 96,256)( 97,255)
( 98,259)( 99,258)(100,262)(101,261)(102,260)(103,269)(104,268)(105,272)
(106,271)(107,270)(108,264)(109,263)(110,267)(111,266)(112,265)(113,279)
(114,278)(115,282)(116,281)(117,280)(118,274)(119,273)(120,277)(121,276)
(122,275)(123,304)(124,303)(125,307)(126,306)(127,305)(128,309)(129,308)
(130,312)(131,311)(132,310)(133,314)(134,313)(135,317)(136,316)(137,315)
(138,319)(139,318)(140,322)(141,321)(142,320)(143,284)(144,283)(145,287)
(146,286)(147,285)(148,289)(149,288)(150,292)(151,291)(152,290)(153,294)
(154,293)(155,297)(156,296)(157,295)(158,299)(159,298)(160,302)(161,301)
(162,300);
s4 := 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);
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*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope