Polytope of Type {2,10,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,4}*1280b
if this polytope has a name.
Group : SmallGroup(1280,1116461)
Rank : 4
Schlafli Type : {2,10,4}
Number of vertices, edges, etc : 2, 80, 160, 32
Order of s0s1s2s3 : 10
Order of s0s1s2s3s2s1 : 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 : {2,5,4}*640, {2,10,4}*640a, {2,10,4}*640b
4-fold quotients : {2,5,4}*320
16-fold quotients : {2,10,2}*80
32-fold quotients : {2,5,2}*40
80-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 13)( 5, 16)( 6, 10)( 8, 17)( 9, 12)( 11, 15)( 19, 67)( 20, 77)
( 21, 80)( 22, 74)( 23, 71)( 24, 81)( 25, 76)( 26, 70)( 27, 79)( 28, 73)
( 29, 68)( 30, 78)( 31, 75)( 32, 69)( 33, 72)( 34, 82)( 35, 51)( 36, 61)
( 37, 64)( 38, 58)( 39, 55)( 40, 65)( 41, 60)( 42, 54)( 43, 63)( 44, 57)
( 45, 52)( 46, 62)( 47, 59)( 48, 53)( 49, 56)( 50, 66)( 84, 93)( 85, 96)
( 86, 90)( 88, 97)( 89, 92)( 91, 95)( 99,147)(100,157)(101,160)(102,154)
(103,151)(104,161)(105,156)(106,150)(107,159)(108,153)(109,148)(110,158)
(111,155)(112,149)(113,152)(114,162)(115,131)(116,141)(117,144)(118,138)
(119,135)(120,145)(121,140)(122,134)(123,143)(124,137)(125,132)(126,142)
(127,139)(128,133)(129,136)(130,146)(164,173)(165,176)(166,170)(168,177)
(169,172)(171,175)(179,227)(180,237)(181,240)(182,234)(183,231)(184,241)
(185,236)(186,230)(187,239)(188,233)(189,228)(190,238)(191,235)(192,229)
(193,232)(194,242)(195,211)(196,221)(197,224)(198,218)(199,215)(200,225)
(201,220)(202,214)(203,223)(204,217)(205,212)(206,222)(207,219)(208,213)
(209,216)(210,226)(244,253)(245,256)(246,250)(248,257)(249,252)(251,255)
(259,307)(260,317)(261,320)(262,314)(263,311)(264,321)(265,316)(266,310)
(267,319)(268,313)(269,308)(270,318)(271,315)(272,309)(273,312)(274,322)
(275,291)(276,301)(277,304)(278,298)(279,295)(280,305)(281,300)(282,294)
(283,303)(284,297)(285,292)(286,302)(287,299)(288,293)(289,296)(290,306);;
s2 := ( 3,179)( 4,194)( 5,181)( 6,192)( 7,185)( 8,188)( 9,183)( 10,190)
( 11,189)( 12,184)( 13,187)( 14,186)( 15,191)( 16,182)( 17,193)( 18,180)
( 19,163)( 20,178)( 21,165)( 22,176)( 23,169)( 24,172)( 25,167)( 26,174)
( 27,173)( 28,168)( 29,171)( 30,170)( 31,175)( 32,166)( 33,177)( 34,164)
( 35,227)( 36,242)( 37,229)( 38,240)( 39,233)( 40,236)( 41,231)( 42,238)
( 43,237)( 44,232)( 45,235)( 46,234)( 47,239)( 48,230)( 49,241)( 50,228)
( 51,211)( 52,226)( 53,213)( 54,224)( 55,217)( 56,220)( 57,215)( 58,222)
( 59,221)( 60,216)( 61,219)( 62,218)( 63,223)( 64,214)( 65,225)( 66,212)
( 67,195)( 68,210)( 69,197)( 70,208)( 71,201)( 72,204)( 73,199)( 74,206)
( 75,205)( 76,200)( 77,203)( 78,202)( 79,207)( 80,198)( 81,209)( 82,196)
( 83,259)( 84,274)( 85,261)( 86,272)( 87,265)( 88,268)( 89,263)( 90,270)
( 91,269)( 92,264)( 93,267)( 94,266)( 95,271)( 96,262)( 97,273)( 98,260)
( 99,243)(100,258)(101,245)(102,256)(103,249)(104,252)(105,247)(106,254)
(107,253)(108,248)(109,251)(110,250)(111,255)(112,246)(113,257)(114,244)
(115,307)(116,322)(117,309)(118,320)(119,313)(120,316)(121,311)(122,318)
(123,317)(124,312)(125,315)(126,314)(127,319)(128,310)(129,321)(130,308)
(131,291)(132,306)(133,293)(134,304)(135,297)(136,300)(137,295)(138,302)
(139,301)(140,296)(141,299)(142,298)(143,303)(144,294)(145,305)(146,292)
(147,275)(148,290)(149,277)(150,288)(151,281)(152,284)(153,279)(154,286)
(155,285)(156,280)(157,283)(158,282)(159,287)(160,278)(161,289)(162,276);;
s3 := ( 3, 87)( 4, 88)( 5, 89)( 6, 90)( 7, 83)( 8, 84)( 9, 85)( 10, 86)
( 11, 95)( 12, 96)( 13, 97)( 14, 98)( 15, 91)( 16, 92)( 17, 93)( 18, 94)
( 19,103)( 20,104)( 21,105)( 22,106)( 23, 99)( 24,100)( 25,101)( 26,102)
( 27,111)( 28,112)( 29,113)( 30,114)( 31,107)( 32,108)( 33,109)( 34,110)
( 35,119)( 36,120)( 37,121)( 38,122)( 39,115)( 40,116)( 41,117)( 42,118)
( 43,127)( 44,128)( 45,129)( 46,130)( 47,123)( 48,124)( 49,125)( 50,126)
( 51,135)( 52,136)( 53,137)( 54,138)( 55,131)( 56,132)( 57,133)( 58,134)
( 59,143)( 60,144)( 61,145)( 62,146)( 63,139)( 64,140)( 65,141)( 66,142)
( 67,151)( 68,152)( 69,153)( 70,154)( 71,147)( 72,148)( 73,149)( 74,150)
( 75,159)( 76,160)( 77,161)( 78,162)( 79,155)( 80,156)( 81,157)( 82,158)
(163,247)(164,248)(165,249)(166,250)(167,243)(168,244)(169,245)(170,246)
(171,255)(172,256)(173,257)(174,258)(175,251)(176,252)(177,253)(178,254)
(179,263)(180,264)(181,265)(182,266)(183,259)(184,260)(185,261)(186,262)
(187,271)(188,272)(189,273)(190,274)(191,267)(192,268)(193,269)(194,270)
(195,279)(196,280)(197,281)(198,282)(199,275)(200,276)(201,277)(202,278)
(203,287)(204,288)(205,289)(206,290)(207,283)(208,284)(209,285)(210,286)
(211,295)(212,296)(213,297)(214,298)(215,291)(216,292)(217,293)(218,294)
(219,303)(220,304)(221,305)(222,306)(223,299)(224,300)(225,301)(226,302)
(227,311)(228,312)(229,313)(230,314)(231,307)(232,308)(233,309)(234,310)
(235,319)(236,320)(237,321)(238,322)(239,315)(240,316)(241,317)(242,318);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(322)!(1,2);
s1 := Sym(322)!( 4, 13)( 5, 16)( 6, 10)( 8, 17)( 9, 12)( 11, 15)( 19, 67)
( 20, 77)( 21, 80)( 22, 74)( 23, 71)( 24, 81)( 25, 76)( 26, 70)( 27, 79)
( 28, 73)( 29, 68)( 30, 78)( 31, 75)( 32, 69)( 33, 72)( 34, 82)( 35, 51)
( 36, 61)( 37, 64)( 38, 58)( 39, 55)( 40, 65)( 41, 60)( 42, 54)( 43, 63)
( 44, 57)( 45, 52)( 46, 62)( 47, 59)( 48, 53)( 49, 56)( 50, 66)( 84, 93)
( 85, 96)( 86, 90)( 88, 97)( 89, 92)( 91, 95)( 99,147)(100,157)(101,160)
(102,154)(103,151)(104,161)(105,156)(106,150)(107,159)(108,153)(109,148)
(110,158)(111,155)(112,149)(113,152)(114,162)(115,131)(116,141)(117,144)
(118,138)(119,135)(120,145)(121,140)(122,134)(123,143)(124,137)(125,132)
(126,142)(127,139)(128,133)(129,136)(130,146)(164,173)(165,176)(166,170)
(168,177)(169,172)(171,175)(179,227)(180,237)(181,240)(182,234)(183,231)
(184,241)(185,236)(186,230)(187,239)(188,233)(189,228)(190,238)(191,235)
(192,229)(193,232)(194,242)(195,211)(196,221)(197,224)(198,218)(199,215)
(200,225)(201,220)(202,214)(203,223)(204,217)(205,212)(206,222)(207,219)
(208,213)(209,216)(210,226)(244,253)(245,256)(246,250)(248,257)(249,252)
(251,255)(259,307)(260,317)(261,320)(262,314)(263,311)(264,321)(265,316)
(266,310)(267,319)(268,313)(269,308)(270,318)(271,315)(272,309)(273,312)
(274,322)(275,291)(276,301)(277,304)(278,298)(279,295)(280,305)(281,300)
(282,294)(283,303)(284,297)(285,292)(286,302)(287,299)(288,293)(289,296)
(290,306);
s2 := Sym(322)!( 3,179)( 4,194)( 5,181)( 6,192)( 7,185)( 8,188)( 9,183)
( 10,190)( 11,189)( 12,184)( 13,187)( 14,186)( 15,191)( 16,182)( 17,193)
( 18,180)( 19,163)( 20,178)( 21,165)( 22,176)( 23,169)( 24,172)( 25,167)
( 26,174)( 27,173)( 28,168)( 29,171)( 30,170)( 31,175)( 32,166)( 33,177)
( 34,164)( 35,227)( 36,242)( 37,229)( 38,240)( 39,233)( 40,236)( 41,231)
( 42,238)( 43,237)( 44,232)( 45,235)( 46,234)( 47,239)( 48,230)( 49,241)
( 50,228)( 51,211)( 52,226)( 53,213)( 54,224)( 55,217)( 56,220)( 57,215)
( 58,222)( 59,221)( 60,216)( 61,219)( 62,218)( 63,223)( 64,214)( 65,225)
( 66,212)( 67,195)( 68,210)( 69,197)( 70,208)( 71,201)( 72,204)( 73,199)
( 74,206)( 75,205)( 76,200)( 77,203)( 78,202)( 79,207)( 80,198)( 81,209)
( 82,196)( 83,259)( 84,274)( 85,261)( 86,272)( 87,265)( 88,268)( 89,263)
( 90,270)( 91,269)( 92,264)( 93,267)( 94,266)( 95,271)( 96,262)( 97,273)
( 98,260)( 99,243)(100,258)(101,245)(102,256)(103,249)(104,252)(105,247)
(106,254)(107,253)(108,248)(109,251)(110,250)(111,255)(112,246)(113,257)
(114,244)(115,307)(116,322)(117,309)(118,320)(119,313)(120,316)(121,311)
(122,318)(123,317)(124,312)(125,315)(126,314)(127,319)(128,310)(129,321)
(130,308)(131,291)(132,306)(133,293)(134,304)(135,297)(136,300)(137,295)
(138,302)(139,301)(140,296)(141,299)(142,298)(143,303)(144,294)(145,305)
(146,292)(147,275)(148,290)(149,277)(150,288)(151,281)(152,284)(153,279)
(154,286)(155,285)(156,280)(157,283)(158,282)(159,287)(160,278)(161,289)
(162,276);
s3 := Sym(322)!( 3, 87)( 4, 88)( 5, 89)( 6, 90)( 7, 83)( 8, 84)( 9, 85)
( 10, 86)( 11, 95)( 12, 96)( 13, 97)( 14, 98)( 15, 91)( 16, 92)( 17, 93)
( 18, 94)( 19,103)( 20,104)( 21,105)( 22,106)( 23, 99)( 24,100)( 25,101)
( 26,102)( 27,111)( 28,112)( 29,113)( 30,114)( 31,107)( 32,108)( 33,109)
( 34,110)( 35,119)( 36,120)( 37,121)( 38,122)( 39,115)( 40,116)( 41,117)
( 42,118)( 43,127)( 44,128)( 45,129)( 46,130)( 47,123)( 48,124)( 49,125)
( 50,126)( 51,135)( 52,136)( 53,137)( 54,138)( 55,131)( 56,132)( 57,133)
( 58,134)( 59,143)( 60,144)( 61,145)( 62,146)( 63,139)( 64,140)( 65,141)
( 66,142)( 67,151)( 68,152)( 69,153)( 70,154)( 71,147)( 72,148)( 73,149)
( 74,150)( 75,159)( 76,160)( 77,161)( 78,162)( 79,155)( 80,156)( 81,157)
( 82,158)(163,247)(164,248)(165,249)(166,250)(167,243)(168,244)(169,245)
(170,246)(171,255)(172,256)(173,257)(174,258)(175,251)(176,252)(177,253)
(178,254)(179,263)(180,264)(181,265)(182,266)(183,259)(184,260)(185,261)
(186,262)(187,271)(188,272)(189,273)(190,274)(191,267)(192,268)(193,269)
(194,270)(195,279)(196,280)(197,281)(198,282)(199,275)(200,276)(201,277)
(202,278)(203,287)(204,288)(205,289)(206,290)(207,283)(208,284)(209,285)
(210,286)(211,295)(212,296)(213,297)(214,298)(215,291)(216,292)(217,293)
(218,294)(219,303)(220,304)(221,305)(222,306)(223,299)(224,300)(225,301)
(226,302)(227,311)(228,312)(229,313)(230,314)(231,307)(232,308)(233,309)
(234,310)(235,319)(236,320)(237,321)(238,322)(239,315)(240,316)(241,317)
(242,318);
poly := sub<Sym(322)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope