Overview
- Group
- SmallGroup(1512,561)
- Rank
- 4
- Schläfli Type
- {21,6,6}
- Vertices, edges, …
- 21, 63, 18, 6
- Order of s0s1s2s3
- 42
- Order of s0s1s2s3s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
6-fold
7-fold
9-fold
14-fold
18-fold
21-fold
27-fold
42-fold
63-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4, 19)( 5, 21)( 6, 20)( 7, 16)( 8, 18)( 9, 17)( 10, 13)( 11, 15)( 12, 14)( 22, 43)( 23, 45)( 24, 44)( 25, 61)( 26, 63)( 27, 62)( 28, 58)( 29, 60)( 30, 59)( 31, 55)( 32, 57)( 33, 56)( 34, 52)( 35, 54)( 36, 53)( 37, 49)( 38, 51)( 39, 50)( 40, 46)( 41, 48)( 42, 47)( 65, 66)( 67, 82)( 68, 84)( 69, 83)( 70, 79)( 71, 81)( 72, 80)( 73, 76)( 74, 78)( 75, 77)( 85,106)( 86,108)( 87,107)( 88,124)( 89,126)( 90,125)( 91,121)( 92,123)( 93,122)( 94,118)( 95,120)( 96,119)( 97,115)( 98,117)( 99,116)(100,112)(101,114)(102,113)(103,109)(104,111)(105,110)(128,129)(130,145)(131,147)(132,146)(133,142)(134,144)(135,143)(136,139)(137,141)(138,140)(148,169)(149,171)(150,170)(151,187)(152,189)(153,188)(154,184)(155,186)(156,185)(157,181)(158,183)(159,182)(160,178)(161,180)(162,179)(163,175)(164,177)(165,176)(166,172)(167,174)(168,173)(191,192)(193,208)(194,210)(195,209)(196,205)(197,207)(198,206)(199,202)(200,204)(201,203)(211,232)(212,234)(213,233)(214,250)(215,252)(216,251)(217,247)(218,249)(219,248)(220,244)(221,246)(222,245)(223,241)(224,243)(225,242)(226,238)(227,240)(228,239)(229,235)(230,237)(231,236)(254,255)(256,271)(257,273)(258,272)(259,268)(260,270)(261,269)(262,265)(263,267)(264,266)(274,295)(275,297)(276,296)(277,313)(278,315)(279,314)(280,310)(281,312)(282,311)(283,307)(284,309)(285,308)(286,304)(287,306)(288,305)(289,301)(290,303)(291,302)(292,298)(293,300)(294,299)(317,318)(319,334)(320,336)(321,335)(322,331)(323,333)(324,332)(325,328)(326,330)(327,329)(337,358)(338,360)(339,359)(340,376)(341,378)(342,377)(343,373)(344,375)(345,374)(346,370)(347,372)(348,371)(349,367)(350,369)(351,368)(352,364)(353,366)(354,365)(355,361)(356,363)(357,362);; s1 := ( 1, 25)( 2, 27)( 3, 26)( 4, 22)( 5, 24)( 6, 23)( 7, 40)( 8, 42)( 9, 41)( 10, 37)( 11, 39)( 12, 38)( 13, 34)( 14, 36)( 15, 35)( 16, 31)( 17, 33)( 18, 32)( 19, 28)( 20, 30)( 21, 29)( 43, 46)( 44, 48)( 45, 47)( 49, 61)( 50, 63)( 51, 62)( 52, 58)( 53, 60)( 54, 59)( 56, 57)( 64, 88)( 65, 90)( 66, 89)( 67, 85)( 68, 87)( 69, 86)( 70,103)( 71,105)( 72,104)( 73,100)( 74,102)( 75,101)( 76, 97)( 77, 99)( 78, 98)( 79, 94)( 80, 96)( 81, 95)( 82, 91)( 83, 93)( 84, 92)(106,109)(107,111)(108,110)(112,124)(113,126)(114,125)(115,121)(116,123)(117,122)(119,120)(127,151)(128,153)(129,152)(130,148)(131,150)(132,149)(133,166)(134,168)(135,167)(136,163)(137,165)(138,164)(139,160)(140,162)(141,161)(142,157)(143,159)(144,158)(145,154)(146,156)(147,155)(169,172)(170,174)(171,173)(175,187)(176,189)(177,188)(178,184)(179,186)(180,185)(182,183)(190,214)(191,216)(192,215)(193,211)(194,213)(195,212)(196,229)(197,231)(198,230)(199,226)(200,228)(201,227)(202,223)(203,225)(204,224)(205,220)(206,222)(207,221)(208,217)(209,219)(210,218)(232,235)(233,237)(234,236)(238,250)(239,252)(240,251)(241,247)(242,249)(243,248)(245,246)(253,277)(254,279)(255,278)(256,274)(257,276)(258,275)(259,292)(260,294)(261,293)(262,289)(263,291)(264,290)(265,286)(266,288)(267,287)(268,283)(269,285)(270,284)(271,280)(272,282)(273,281)(295,298)(296,300)(297,299)(301,313)(302,315)(303,314)(304,310)(305,312)(306,311)(308,309)(316,340)(317,342)(318,341)(319,337)(320,339)(321,338)(322,355)(323,357)(324,356)(325,352)(326,354)(327,353)(328,349)(329,351)(330,350)(331,346)(332,348)(333,347)(334,343)(335,345)(336,344)(358,361)(359,363)(360,362)(364,376)(365,378)(366,377)(367,373)(368,375)(369,374)(371,372);; s2 := ( 1, 64)( 2, 66)( 3, 65)( 4, 67)( 5, 69)( 6, 68)( 7, 70)( 8, 72)( 9, 71)( 10, 73)( 11, 75)( 12, 74)( 13, 76)( 14, 78)( 15, 77)( 16, 79)( 17, 81)( 18, 80)( 19, 82)( 20, 84)( 21, 83)( 22, 86)( 23, 85)( 24, 87)( 25, 89)( 26, 88)( 27, 90)( 28, 92)( 29, 91)( 30, 93)( 31, 95)( 32, 94)( 33, 96)( 34, 98)( 35, 97)( 36, 99)( 37,101)( 38,100)( 39,102)( 40,104)( 41,103)( 42,105)( 43,108)( 44,107)( 45,106)( 46,111)( 47,110)( 48,109)( 49,114)( 50,113)( 51,112)( 52,117)( 53,116)( 54,115)( 55,120)( 56,119)( 57,118)( 58,123)( 59,122)( 60,121)( 61,126)( 62,125)( 63,124)(128,129)(131,132)(134,135)(137,138)(140,141)(143,144)(146,147)(148,149)(151,152)(154,155)(157,158)(160,161)(163,164)(166,167)(169,171)(172,174)(175,177)(178,180)(181,183)(184,186)(187,189)(190,253)(191,255)(192,254)(193,256)(194,258)(195,257)(196,259)(197,261)(198,260)(199,262)(200,264)(201,263)(202,265)(203,267)(204,266)(205,268)(206,270)(207,269)(208,271)(209,273)(210,272)(211,275)(212,274)(213,276)(214,278)(215,277)(216,279)(217,281)(218,280)(219,282)(220,284)(221,283)(222,285)(223,287)(224,286)(225,288)(226,290)(227,289)(228,291)(229,293)(230,292)(231,294)(232,297)(233,296)(234,295)(235,300)(236,299)(237,298)(238,303)(239,302)(240,301)(241,306)(242,305)(243,304)(244,309)(245,308)(246,307)(247,312)(248,311)(249,310)(250,315)(251,314)(252,313)(317,318)(320,321)(323,324)(326,327)(329,330)(332,333)(335,336)(337,338)(340,341)(343,344)(346,347)(349,350)(352,353)(355,356)(358,360)(361,363)(364,366)(367,369)(370,372)(373,375)(376,378);; s3 := ( 1,190)( 2,192)( 3,191)( 4,193)( 5,195)( 6,194)( 7,196)( 8,198)( 9,197)( 10,199)( 11,201)( 12,200)( 13,202)( 14,204)( 15,203)( 16,205)( 17,207)( 18,206)( 19,208)( 20,210)( 21,209)( 22,211)( 23,213)( 24,212)( 25,214)( 26,216)( 27,215)( 28,217)( 29,219)( 30,218)( 31,220)( 32,222)( 33,221)( 34,223)( 35,225)( 36,224)( 37,226)( 38,228)( 39,227)( 40,229)( 41,231)( 42,230)( 43,232)( 44,234)( 45,233)( 46,235)( 47,237)( 48,236)( 49,238)( 50,240)( 51,239)( 52,241)( 53,243)( 54,242)( 55,244)( 56,246)( 57,245)( 58,247)( 59,249)( 60,248)( 61,250)( 62,252)( 63,251)( 64,316)( 65,318)( 66,317)( 67,319)( 68,321)( 69,320)( 70,322)( 71,324)( 72,323)( 73,325)( 74,327)( 75,326)( 76,328)( 77,330)( 78,329)( 79,331)( 80,333)( 81,332)( 82,334)( 83,336)( 84,335)( 85,337)( 86,339)( 87,338)( 88,340)( 89,342)( 90,341)( 91,343)( 92,345)( 93,344)( 94,346)( 95,348)( 96,347)( 97,349)( 98,351)( 99,350)(100,352)(101,354)(102,353)(103,355)(104,357)(105,356)(106,358)(107,360)(108,359)(109,361)(110,363)(111,362)(112,364)(113,366)(114,365)(115,367)(116,369)(117,368)(118,370)(119,372)(120,371)(121,373)(122,375)(123,374)(124,376)(125,378)(126,377)(127,253)(128,255)(129,254)(130,256)(131,258)(132,257)(133,259)(134,261)(135,260)(136,262)(137,264)(138,263)(139,265)(140,267)(141,266)(142,268)(143,270)(144,269)(145,271)(146,273)(147,272)(148,274)(149,276)(150,275)(151,277)(152,279)(153,278)(154,280)(155,282)(156,281)(157,283)(158,285)(159,284)(160,286)(161,288)(162,287)(163,289)(164,291)(165,290)(166,292)(167,294)(168,293)(169,295)(170,297)(171,296)(172,298)(173,300)(174,299)(175,301)(176,303)(177,302)(178,304)(179,306)(180,305)(181,307)(182,309)(183,308)(184,310)(185,312)(186,311)(187,313)(188,315)(189,314);; 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*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(378)!( 2, 3)( 4, 19)( 5, 21)( 6, 20)( 7, 16)( 8, 18)( 9, 17)( 10, 13)( 11, 15)( 12, 14)( 22, 43)( 23, 45)( 24, 44)( 25, 61)( 26, 63)( 27, 62)( 28, 58)( 29, 60)( 30, 59)( 31, 55)( 32, 57)( 33, 56)( 34, 52)( 35, 54)( 36, 53)( 37, 49)( 38, 51)( 39, 50)( 40, 46)( 41, 48)( 42, 47)( 65, 66)( 67, 82)( 68, 84)( 69, 83)( 70, 79)( 71, 81)( 72, 80)( 73, 76)( 74, 78)( 75, 77)( 85,106)( 86,108)( 87,107)( 88,124)( 89,126)( 90,125)( 91,121)( 92,123)( 93,122)( 94,118)( 95,120)( 96,119)( 97,115)( 98,117)( 99,116)(100,112)(101,114)(102,113)(103,109)(104,111)(105,110)(128,129)(130,145)(131,147)(132,146)(133,142)(134,144)(135,143)(136,139)(137,141)(138,140)(148,169)(149,171)(150,170)(151,187)(152,189)(153,188)(154,184)(155,186)(156,185)(157,181)(158,183)(159,182)(160,178)(161,180)(162,179)(163,175)(164,177)(165,176)(166,172)(167,174)(168,173)(191,192)(193,208)(194,210)(195,209)(196,205)(197,207)(198,206)(199,202)(200,204)(201,203)(211,232)(212,234)(213,233)(214,250)(215,252)(216,251)(217,247)(218,249)(219,248)(220,244)(221,246)(222,245)(223,241)(224,243)(225,242)(226,238)(227,240)(228,239)(229,235)(230,237)(231,236)(254,255)(256,271)(257,273)(258,272)(259,268)(260,270)(261,269)(262,265)(263,267)(264,266)(274,295)(275,297)(276,296)(277,313)(278,315)(279,314)(280,310)(281,312)(282,311)(283,307)(284,309)(285,308)(286,304)(287,306)(288,305)(289,301)(290,303)(291,302)(292,298)(293,300)(294,299)(317,318)(319,334)(320,336)(321,335)(322,331)(323,333)(324,332)(325,328)(326,330)(327,329)(337,358)(338,360)(339,359)(340,376)(341,378)(342,377)(343,373)(344,375)(345,374)(346,370)(347,372)(348,371)(349,367)(350,369)(351,368)(352,364)(353,366)(354,365)(355,361)(356,363)(357,362); s1 := Sym(378)!( 1, 25)( 2, 27)( 3, 26)( 4, 22)( 5, 24)( 6, 23)( 7, 40)( 8, 42)( 9, 41)( 10, 37)( 11, 39)( 12, 38)( 13, 34)( 14, 36)( 15, 35)( 16, 31)( 17, 33)( 18, 32)( 19, 28)( 20, 30)( 21, 29)( 43, 46)( 44, 48)( 45, 47)( 49, 61)( 50, 63)( 51, 62)( 52, 58)( 53, 60)( 54, 59)( 56, 57)( 64, 88)( 65, 90)( 66, 89)( 67, 85)( 68, 87)( 69, 86)( 70,103)( 71,105)( 72,104)( 73,100)( 74,102)( 75,101)( 76, 97)( 77, 99)( 78, 98)( 79, 94)( 80, 96)( 81, 95)( 82, 91)( 83, 93)( 84, 92)(106,109)(107,111)(108,110)(112,124)(113,126)(114,125)(115,121)(116,123)(117,122)(119,120)(127,151)(128,153)(129,152)(130,148)(131,150)(132,149)(133,166)(134,168)(135,167)(136,163)(137,165)(138,164)(139,160)(140,162)(141,161)(142,157)(143,159)(144,158)(145,154)(146,156)(147,155)(169,172)(170,174)(171,173)(175,187)(176,189)(177,188)(178,184)(179,186)(180,185)(182,183)(190,214)(191,216)(192,215)(193,211)(194,213)(195,212)(196,229)(197,231)(198,230)(199,226)(200,228)(201,227)(202,223)(203,225)(204,224)(205,220)(206,222)(207,221)(208,217)(209,219)(210,218)(232,235)(233,237)(234,236)(238,250)(239,252)(240,251)(241,247)(242,249)(243,248)(245,246)(253,277)(254,279)(255,278)(256,274)(257,276)(258,275)(259,292)(260,294)(261,293)(262,289)(263,291)(264,290)(265,286)(266,288)(267,287)(268,283)(269,285)(270,284)(271,280)(272,282)(273,281)(295,298)(296,300)(297,299)(301,313)(302,315)(303,314)(304,310)(305,312)(306,311)(308,309)(316,340)(317,342)(318,341)(319,337)(320,339)(321,338)(322,355)(323,357)(324,356)(325,352)(326,354)(327,353)(328,349)(329,351)(330,350)(331,346)(332,348)(333,347)(334,343)(335,345)(336,344)(358,361)(359,363)(360,362)(364,376)(365,378)(366,377)(367,373)(368,375)(369,374)(371,372); s2 := Sym(378)!( 1, 64)( 2, 66)( 3, 65)( 4, 67)( 5, 69)( 6, 68)( 7, 70)( 8, 72)( 9, 71)( 10, 73)( 11, 75)( 12, 74)( 13, 76)( 14, 78)( 15, 77)( 16, 79)( 17, 81)( 18, 80)( 19, 82)( 20, 84)( 21, 83)( 22, 86)( 23, 85)( 24, 87)( 25, 89)( 26, 88)( 27, 90)( 28, 92)( 29, 91)( 30, 93)( 31, 95)( 32, 94)( 33, 96)( 34, 98)( 35, 97)( 36, 99)( 37,101)( 38,100)( 39,102)( 40,104)( 41,103)( 42,105)( 43,108)( 44,107)( 45,106)( 46,111)( 47,110)( 48,109)( 49,114)( 50,113)( 51,112)( 52,117)( 53,116)( 54,115)( 55,120)( 56,119)( 57,118)( 58,123)( 59,122)( 60,121)( 61,126)( 62,125)( 63,124)(128,129)(131,132)(134,135)(137,138)(140,141)(143,144)(146,147)(148,149)(151,152)(154,155)(157,158)(160,161)(163,164)(166,167)(169,171)(172,174)(175,177)(178,180)(181,183)(184,186)(187,189)(190,253)(191,255)(192,254)(193,256)(194,258)(195,257)(196,259)(197,261)(198,260)(199,262)(200,264)(201,263)(202,265)(203,267)(204,266)(205,268)(206,270)(207,269)(208,271)(209,273)(210,272)(211,275)(212,274)(213,276)(214,278)(215,277)(216,279)(217,281)(218,280)(219,282)(220,284)(221,283)(222,285)(223,287)(224,286)(225,288)(226,290)(227,289)(228,291)(229,293)(230,292)(231,294)(232,297)(233,296)(234,295)(235,300)(236,299)(237,298)(238,303)(239,302)(240,301)(241,306)(242,305)(243,304)(244,309)(245,308)(246,307)(247,312)(248,311)(249,310)(250,315)(251,314)(252,313)(317,318)(320,321)(323,324)(326,327)(329,330)(332,333)(335,336)(337,338)(340,341)(343,344)(346,347)(349,350)(352,353)(355,356)(358,360)(361,363)(364,366)(367,369)(370,372)(373,375)(376,378); s3 := Sym(378)!( 1,190)( 2,192)( 3,191)( 4,193)( 5,195)( 6,194)( 7,196)( 8,198)( 9,197)( 10,199)( 11,201)( 12,200)( 13,202)( 14,204)( 15,203)( 16,205)( 17,207)( 18,206)( 19,208)( 20,210)( 21,209)( 22,211)( 23,213)( 24,212)( 25,214)( 26,216)( 27,215)( 28,217)( 29,219)( 30,218)( 31,220)( 32,222)( 33,221)( 34,223)( 35,225)( 36,224)( 37,226)( 38,228)( 39,227)( 40,229)( 41,231)( 42,230)( 43,232)( 44,234)( 45,233)( 46,235)( 47,237)( 48,236)( 49,238)( 50,240)( 51,239)( 52,241)( 53,243)( 54,242)( 55,244)( 56,246)( 57,245)( 58,247)( 59,249)( 60,248)( 61,250)( 62,252)( 63,251)( 64,316)( 65,318)( 66,317)( 67,319)( 68,321)( 69,320)( 70,322)( 71,324)( 72,323)( 73,325)( 74,327)( 75,326)( 76,328)( 77,330)( 78,329)( 79,331)( 80,333)( 81,332)( 82,334)( 83,336)( 84,335)( 85,337)( 86,339)( 87,338)( 88,340)( 89,342)( 90,341)( 91,343)( 92,345)( 93,344)( 94,346)( 95,348)( 96,347)( 97,349)( 98,351)( 99,350)(100,352)(101,354)(102,353)(103,355)(104,357)(105,356)(106,358)(107,360)(108,359)(109,361)(110,363)(111,362)(112,364)(113,366)(114,365)(115,367)(116,369)(117,368)(118,370)(119,372)(120,371)(121,373)(122,375)(123,374)(124,376)(125,378)(126,377)(127,253)(128,255)(129,254)(130,256)(131,258)(132,257)(133,259)(134,261)(135,260)(136,262)(137,264)(138,263)(139,265)(140,267)(141,266)(142,268)(143,270)(144,269)(145,271)(146,273)(147,272)(148,274)(149,276)(150,275)(151,277)(152,279)(153,278)(154,280)(155,282)(156,281)(157,283)(158,285)(159,284)(160,286)(161,288)(162,287)(163,289)(164,291)(165,290)(166,292)(167,294)(168,293)(169,295)(170,297)(171,296)(172,298)(173,300)(174,299)(175,301)(176,303)(177,302)(178,304)(179,306)(180,305)(181,307)(182,309)(183,308)(184,310)(185,312)(186,311)(187,313)(188,315)(189,314); poly := sub<Sym(378)|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*s0*s1*s2*s1*s2*s0*s1*s2*s1, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.