Polytope of Type {20,4,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,4,2}*1280c
if this polytope has a name.
Group : SmallGroup(1280,1116447)
Rank : 4
Schlafli Type : {20,4,2}
Number of vertices, edges, etc : 80, 160, 16, 2
Order of s0s1s2s3 : 20
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-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 : {10,4,2}*640a
4-fold quotients : {5,4,2}*320
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 9)( 3, 16)( 4, 8)( 6, 13)( 7, 12)( 11, 15)( 17, 65)( 18, 73)
( 19, 80)( 20, 72)( 21, 69)( 22, 77)( 23, 76)( 24, 68)( 25, 66)( 26, 74)
( 27, 79)( 28, 71)( 29, 70)( 30, 78)( 31, 75)( 32, 67)( 33, 49)( 34, 57)
( 35, 64)( 36, 56)( 37, 53)( 38, 61)( 39, 60)( 40, 52)( 41, 50)( 42, 58)
( 43, 63)( 44, 55)( 45, 54)( 46, 62)( 47, 59)( 48, 51)( 82, 89)( 83, 96)
( 84, 88)( 86, 93)( 87, 92)( 91, 95)( 97,145)( 98,153)( 99,160)(100,152)
(101,149)(102,157)(103,156)(104,148)(105,146)(106,154)(107,159)(108,151)
(109,150)(110,158)(111,155)(112,147)(113,129)(114,137)(115,144)(116,136)
(117,133)(118,141)(119,140)(120,132)(121,130)(122,138)(123,143)(124,135)
(125,134)(126,142)(127,139)(128,131)(161,241)(162,249)(163,256)(164,248)
(165,245)(166,253)(167,252)(168,244)(169,242)(170,250)(171,255)(172,247)
(173,246)(174,254)(175,251)(176,243)(177,305)(178,313)(179,320)(180,312)
(181,309)(182,317)(183,316)(184,308)(185,306)(186,314)(187,319)(188,311)
(189,310)(190,318)(191,315)(192,307)(193,289)(194,297)(195,304)(196,296)
(197,293)(198,301)(199,300)(200,292)(201,290)(202,298)(203,303)(204,295)
(205,294)(206,302)(207,299)(208,291)(209,273)(210,281)(211,288)(212,280)
(213,277)(214,285)(215,284)(216,276)(217,274)(218,282)(219,287)(220,279)
(221,278)(222,286)(223,283)(224,275)(225,257)(226,265)(227,272)(228,264)
(229,261)(230,269)(231,268)(232,260)(233,258)(234,266)(235,271)(236,263)
(237,262)(238,270)(239,267)(240,259);;
s1 := ( 1,177)( 2,187)( 3,186)( 4,180)( 5,189)( 6,183)( 7,182)( 8,192)
( 9,185)( 10,179)( 11,178)( 12,188)( 13,181)( 14,191)( 15,190)( 16,184)
( 17,161)( 18,171)( 19,170)( 20,164)( 21,173)( 22,167)( 23,166)( 24,176)
( 25,169)( 26,163)( 27,162)( 28,172)( 29,165)( 30,175)( 31,174)( 32,168)
( 33,225)( 34,235)( 35,234)( 36,228)( 37,237)( 38,231)( 39,230)( 40,240)
( 41,233)( 42,227)( 43,226)( 44,236)( 45,229)( 46,239)( 47,238)( 48,232)
( 49,209)( 50,219)( 51,218)( 52,212)( 53,221)( 54,215)( 55,214)( 56,224)
( 57,217)( 58,211)( 59,210)( 60,220)( 61,213)( 62,223)( 63,222)( 64,216)
( 65,193)( 66,203)( 67,202)( 68,196)( 69,205)( 70,199)( 71,198)( 72,208)
( 73,201)( 74,195)( 75,194)( 76,204)( 77,197)( 78,207)( 79,206)( 80,200)
( 81,257)( 82,267)( 83,266)( 84,260)( 85,269)( 86,263)( 87,262)( 88,272)
( 89,265)( 90,259)( 91,258)( 92,268)( 93,261)( 94,271)( 95,270)( 96,264)
( 97,241)( 98,251)( 99,250)(100,244)(101,253)(102,247)(103,246)(104,256)
(105,249)(106,243)(107,242)(108,252)(109,245)(110,255)(111,254)(112,248)
(113,305)(114,315)(115,314)(116,308)(117,317)(118,311)(119,310)(120,320)
(121,313)(122,307)(123,306)(124,316)(125,309)(126,319)(127,318)(128,312)
(129,289)(130,299)(131,298)(132,292)(133,301)(134,295)(135,294)(136,304)
(137,297)(138,291)(139,290)(140,300)(141,293)(142,303)(143,302)(144,296)
(145,273)(146,283)(147,282)(148,276)(149,285)(150,279)(151,278)(152,288)
(153,281)(154,275)(155,274)(156,284)(157,277)(158,287)(159,286)(160,280);;
s2 := ( 1, 85)( 2, 86)( 3, 87)( 4, 88)( 5, 81)( 6, 82)( 7, 83)( 8, 84)
( 9, 93)( 10, 94)( 11, 95)( 12, 96)( 13, 89)( 14, 90)( 15, 91)( 16, 92)
( 17,101)( 18,102)( 19,103)( 20,104)( 21, 97)( 22, 98)( 23, 99)( 24,100)
( 25,109)( 26,110)( 27,111)( 28,112)( 29,105)( 30,106)( 31,107)( 32,108)
( 33,117)( 34,118)( 35,119)( 36,120)( 37,113)( 38,114)( 39,115)( 40,116)
( 41,125)( 42,126)( 43,127)( 44,128)( 45,121)( 46,122)( 47,123)( 48,124)
( 49,133)( 50,134)( 51,135)( 52,136)( 53,129)( 54,130)( 55,131)( 56,132)
( 57,141)( 58,142)( 59,143)( 60,144)( 61,137)( 62,138)( 63,139)( 64,140)
( 65,149)( 66,150)( 67,151)( 68,152)( 69,145)( 70,146)( 71,147)( 72,148)
( 73,157)( 74,158)( 75,159)( 76,160)( 77,153)( 78,154)( 79,155)( 80,156)
(161,245)(162,246)(163,247)(164,248)(165,241)(166,242)(167,243)(168,244)
(169,253)(170,254)(171,255)(172,256)(173,249)(174,250)(175,251)(176,252)
(177,261)(178,262)(179,263)(180,264)(181,257)(182,258)(183,259)(184,260)
(185,269)(186,270)(187,271)(188,272)(189,265)(190,266)(191,267)(192,268)
(193,277)(194,278)(195,279)(196,280)(197,273)(198,274)(199,275)(200,276)
(201,285)(202,286)(203,287)(204,288)(205,281)(206,282)(207,283)(208,284)
(209,293)(210,294)(211,295)(212,296)(213,289)(214,290)(215,291)(216,292)
(217,301)(218,302)(219,303)(220,304)(221,297)(222,298)(223,299)(224,300)
(225,309)(226,310)(227,311)(228,312)(229,305)(230,306)(231,307)(232,308)
(233,317)(234,318)(235,319)(236,320)(237,313)(238,314)(239,315)(240,316);;
s3 := (321,322);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(322)!( 2, 9)( 3, 16)( 4, 8)( 6, 13)( 7, 12)( 11, 15)( 17, 65)
( 18, 73)( 19, 80)( 20, 72)( 21, 69)( 22, 77)( 23, 76)( 24, 68)( 25, 66)
( 26, 74)( 27, 79)( 28, 71)( 29, 70)( 30, 78)( 31, 75)( 32, 67)( 33, 49)
( 34, 57)( 35, 64)( 36, 56)( 37, 53)( 38, 61)( 39, 60)( 40, 52)( 41, 50)
( 42, 58)( 43, 63)( 44, 55)( 45, 54)( 46, 62)( 47, 59)( 48, 51)( 82, 89)
( 83, 96)( 84, 88)( 86, 93)( 87, 92)( 91, 95)( 97,145)( 98,153)( 99,160)
(100,152)(101,149)(102,157)(103,156)(104,148)(105,146)(106,154)(107,159)
(108,151)(109,150)(110,158)(111,155)(112,147)(113,129)(114,137)(115,144)
(116,136)(117,133)(118,141)(119,140)(120,132)(121,130)(122,138)(123,143)
(124,135)(125,134)(126,142)(127,139)(128,131)(161,241)(162,249)(163,256)
(164,248)(165,245)(166,253)(167,252)(168,244)(169,242)(170,250)(171,255)
(172,247)(173,246)(174,254)(175,251)(176,243)(177,305)(178,313)(179,320)
(180,312)(181,309)(182,317)(183,316)(184,308)(185,306)(186,314)(187,319)
(188,311)(189,310)(190,318)(191,315)(192,307)(193,289)(194,297)(195,304)
(196,296)(197,293)(198,301)(199,300)(200,292)(201,290)(202,298)(203,303)
(204,295)(205,294)(206,302)(207,299)(208,291)(209,273)(210,281)(211,288)
(212,280)(213,277)(214,285)(215,284)(216,276)(217,274)(218,282)(219,287)
(220,279)(221,278)(222,286)(223,283)(224,275)(225,257)(226,265)(227,272)
(228,264)(229,261)(230,269)(231,268)(232,260)(233,258)(234,266)(235,271)
(236,263)(237,262)(238,270)(239,267)(240,259);
s1 := Sym(322)!( 1,177)( 2,187)( 3,186)( 4,180)( 5,189)( 6,183)( 7,182)
( 8,192)( 9,185)( 10,179)( 11,178)( 12,188)( 13,181)( 14,191)( 15,190)
( 16,184)( 17,161)( 18,171)( 19,170)( 20,164)( 21,173)( 22,167)( 23,166)
( 24,176)( 25,169)( 26,163)( 27,162)( 28,172)( 29,165)( 30,175)( 31,174)
( 32,168)( 33,225)( 34,235)( 35,234)( 36,228)( 37,237)( 38,231)( 39,230)
( 40,240)( 41,233)( 42,227)( 43,226)( 44,236)( 45,229)( 46,239)( 47,238)
( 48,232)( 49,209)( 50,219)( 51,218)( 52,212)( 53,221)( 54,215)( 55,214)
( 56,224)( 57,217)( 58,211)( 59,210)( 60,220)( 61,213)( 62,223)( 63,222)
( 64,216)( 65,193)( 66,203)( 67,202)( 68,196)( 69,205)( 70,199)( 71,198)
( 72,208)( 73,201)( 74,195)( 75,194)( 76,204)( 77,197)( 78,207)( 79,206)
( 80,200)( 81,257)( 82,267)( 83,266)( 84,260)( 85,269)( 86,263)( 87,262)
( 88,272)( 89,265)( 90,259)( 91,258)( 92,268)( 93,261)( 94,271)( 95,270)
( 96,264)( 97,241)( 98,251)( 99,250)(100,244)(101,253)(102,247)(103,246)
(104,256)(105,249)(106,243)(107,242)(108,252)(109,245)(110,255)(111,254)
(112,248)(113,305)(114,315)(115,314)(116,308)(117,317)(118,311)(119,310)
(120,320)(121,313)(122,307)(123,306)(124,316)(125,309)(126,319)(127,318)
(128,312)(129,289)(130,299)(131,298)(132,292)(133,301)(134,295)(135,294)
(136,304)(137,297)(138,291)(139,290)(140,300)(141,293)(142,303)(143,302)
(144,296)(145,273)(146,283)(147,282)(148,276)(149,285)(150,279)(151,278)
(152,288)(153,281)(154,275)(155,274)(156,284)(157,277)(158,287)(159,286)
(160,280);
s2 := Sym(322)!( 1, 85)( 2, 86)( 3, 87)( 4, 88)( 5, 81)( 6, 82)( 7, 83)
( 8, 84)( 9, 93)( 10, 94)( 11, 95)( 12, 96)( 13, 89)( 14, 90)( 15, 91)
( 16, 92)( 17,101)( 18,102)( 19,103)( 20,104)( 21, 97)( 22, 98)( 23, 99)
( 24,100)( 25,109)( 26,110)( 27,111)( 28,112)( 29,105)( 30,106)( 31,107)
( 32,108)( 33,117)( 34,118)( 35,119)( 36,120)( 37,113)( 38,114)( 39,115)
( 40,116)( 41,125)( 42,126)( 43,127)( 44,128)( 45,121)( 46,122)( 47,123)
( 48,124)( 49,133)( 50,134)( 51,135)( 52,136)( 53,129)( 54,130)( 55,131)
( 56,132)( 57,141)( 58,142)( 59,143)( 60,144)( 61,137)( 62,138)( 63,139)
( 64,140)( 65,149)( 66,150)( 67,151)( 68,152)( 69,145)( 70,146)( 71,147)
( 72,148)( 73,157)( 74,158)( 75,159)( 76,160)( 77,153)( 78,154)( 79,155)
( 80,156)(161,245)(162,246)(163,247)(164,248)(165,241)(166,242)(167,243)
(168,244)(169,253)(170,254)(171,255)(172,256)(173,249)(174,250)(175,251)
(176,252)(177,261)(178,262)(179,263)(180,264)(181,257)(182,258)(183,259)
(184,260)(185,269)(186,270)(187,271)(188,272)(189,265)(190,266)(191,267)
(192,268)(193,277)(194,278)(195,279)(196,280)(197,273)(198,274)(199,275)
(200,276)(201,285)(202,286)(203,287)(204,288)(205,281)(206,282)(207,283)
(208,284)(209,293)(210,294)(211,295)(212,296)(213,289)(214,290)(215,291)
(216,292)(217,301)(218,302)(219,303)(220,304)(221,297)(222,298)(223,299)
(224,300)(225,309)(226,310)(227,311)(228,312)(229,305)(230,306)(231,307)
(232,308)(233,317)(234,318)(235,319)(236,320)(237,313)(238,314)(239,315)
(240,316);
s3 := Sym(322)!(321,322);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2 >;
to this polytope