Overview
- Group
- SmallGroup(840,128)
- Rank
- 2
- Schläfli Type
- {420}
- Vertices, edges, …
- 420, 420
- Order of s0s1
- 420
- Also known as
- 420-gon, {420}. if this polytope has another name.
Special Properties
- Universal
- Spherical
- Locally Spherical
- Orientable
- Self-Dual
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
5-fold
6-fold
7-fold
10-fold
12-fold
14-fold
15-fold
20-fold
21-fold
28-fold
30-fold
35-fold
42-fold
60-fold
70-fold
84-fold
105-fold
140-fold
210-fold
Covers minimal covers in bold
2-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 7)( 3, 6)( 4, 5)( 8, 29)( 9, 35)( 10, 34)( 11, 33)( 12, 32)( 13, 31)( 14, 30)( 15, 22)( 16, 28)( 17, 27)( 18, 26)( 19, 25)( 20, 24)( 21, 23)( 36, 71)( 37, 77)( 38, 76)( 39, 75)( 40, 74)( 41, 73)( 42, 72)( 43, 99)( 44,105)( 45,104)( 46,103)( 47,102)( 48,101)( 49,100)( 50, 92)( 51, 98)( 52, 97)( 53, 96)( 54, 95)( 55, 94)( 56, 93)( 57, 85)( 58, 91)( 59, 90)( 60, 89)( 61, 88)( 62, 87)( 63, 86)( 64, 78)( 65, 84)( 66, 83)( 67, 82)( 68, 81)( 69, 80)( 70, 79)(107,112)(108,111)(109,110)(113,134)(114,140)(115,139)(116,138)(117,137)(118,136)(119,135)(120,127)(121,133)(122,132)(123,131)(124,130)(125,129)(126,128)(141,176)(142,182)(143,181)(144,180)(145,179)(146,178)(147,177)(148,204)(149,210)(150,209)(151,208)(152,207)(153,206)(154,205)(155,197)(156,203)(157,202)(158,201)(159,200)(160,199)(161,198)(162,190)(163,196)(164,195)(165,194)(166,193)(167,192)(168,191)(169,183)(170,189)(171,188)(172,187)(173,186)(174,185)(175,184)(211,316)(212,322)(213,321)(214,320)(215,319)(216,318)(217,317)(218,344)(219,350)(220,349)(221,348)(222,347)(223,346)(224,345)(225,337)(226,343)(227,342)(228,341)(229,340)(230,339)(231,338)(232,330)(233,336)(234,335)(235,334)(236,333)(237,332)(238,331)(239,323)(240,329)(241,328)(242,327)(243,326)(244,325)(245,324)(246,386)(247,392)(248,391)(249,390)(250,389)(251,388)(252,387)(253,414)(254,420)(255,419)(256,418)(257,417)(258,416)(259,415)(260,407)(261,413)(262,412)(263,411)(264,410)(265,409)(266,408)(267,400)(268,406)(269,405)(270,404)(271,403)(272,402)(273,401)(274,393)(275,399)(276,398)(277,397)(278,396)(279,395)(280,394)(281,351)(282,357)(283,356)(284,355)(285,354)(286,353)(287,352)(288,379)(289,385)(290,384)(291,383)(292,382)(293,381)(294,380)(295,372)(296,378)(297,377)(298,376)(299,375)(300,374)(301,373)(302,365)(303,371)(304,370)(305,369)(306,368)(307,367)(308,366)(309,358)(310,364)(311,363)(312,362)(313,361)(314,360)(315,359);; s1 := ( 1,254)( 2,253)( 3,259)( 4,258)( 5,257)( 6,256)( 7,255)( 8,247)( 9,246)( 10,252)( 11,251)( 12,250)( 13,249)( 14,248)( 15,275)( 16,274)( 17,280)( 18,279)( 19,278)( 20,277)( 21,276)( 22,268)( 23,267)( 24,273)( 25,272)( 26,271)( 27,270)( 28,269)( 29,261)( 30,260)( 31,266)( 32,265)( 33,264)( 34,263)( 35,262)( 36,219)( 37,218)( 38,224)( 39,223)( 40,222)( 41,221)( 42,220)( 43,212)( 44,211)( 45,217)( 46,216)( 47,215)( 48,214)( 49,213)( 50,240)( 51,239)( 52,245)( 53,244)( 54,243)( 55,242)( 56,241)( 57,233)( 58,232)( 59,238)( 60,237)( 61,236)( 62,235)( 63,234)( 64,226)( 65,225)( 66,231)( 67,230)( 68,229)( 69,228)( 70,227)( 71,289)( 72,288)( 73,294)( 74,293)( 75,292)( 76,291)( 77,290)( 78,282)( 79,281)( 80,287)( 81,286)( 82,285)( 83,284)( 84,283)( 85,310)( 86,309)( 87,315)( 88,314)( 89,313)( 90,312)( 91,311)( 92,303)( 93,302)( 94,308)( 95,307)( 96,306)( 97,305)( 98,304)( 99,296)(100,295)(101,301)(102,300)(103,299)(104,298)(105,297)(106,359)(107,358)(108,364)(109,363)(110,362)(111,361)(112,360)(113,352)(114,351)(115,357)(116,356)(117,355)(118,354)(119,353)(120,380)(121,379)(122,385)(123,384)(124,383)(125,382)(126,381)(127,373)(128,372)(129,378)(130,377)(131,376)(132,375)(133,374)(134,366)(135,365)(136,371)(137,370)(138,369)(139,368)(140,367)(141,324)(142,323)(143,329)(144,328)(145,327)(146,326)(147,325)(148,317)(149,316)(150,322)(151,321)(152,320)(153,319)(154,318)(155,345)(156,344)(157,350)(158,349)(159,348)(160,347)(161,346)(162,338)(163,337)(164,343)(165,342)(166,341)(167,340)(168,339)(169,331)(170,330)(171,336)(172,335)(173,334)(174,333)(175,332)(176,394)(177,393)(178,399)(179,398)(180,397)(181,396)(182,395)(183,387)(184,386)(185,392)(186,391)(187,390)(188,389)(189,388)(190,415)(191,414)(192,420)(193,419)(194,418)(195,417)(196,416)(197,408)(198,407)(199,413)(200,412)(201,411)(202,410)(203,409)(204,401)(205,400)(206,406)(207,405)(208,404)(209,403)(210,402);; poly := Group([s0,s1]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1");;
s0 := F.1;; s1 := F.2;;
rels := [ s0*s0, s1*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(420)!( 2, 7)( 3, 6)( 4, 5)( 8, 29)( 9, 35)( 10, 34)( 11, 33)( 12, 32)( 13, 31)( 14, 30)( 15, 22)( 16, 28)( 17, 27)( 18, 26)( 19, 25)( 20, 24)( 21, 23)( 36, 71)( 37, 77)( 38, 76)( 39, 75)( 40, 74)( 41, 73)( 42, 72)( 43, 99)( 44,105)( 45,104)( 46,103)( 47,102)( 48,101)( 49,100)( 50, 92)( 51, 98)( 52, 97)( 53, 96)( 54, 95)( 55, 94)( 56, 93)( 57, 85)( 58, 91)( 59, 90)( 60, 89)( 61, 88)( 62, 87)( 63, 86)( 64, 78)( 65, 84)( 66, 83)( 67, 82)( 68, 81)( 69, 80)( 70, 79)(107,112)(108,111)(109,110)(113,134)(114,140)(115,139)(116,138)(117,137)(118,136)(119,135)(120,127)(121,133)(122,132)(123,131)(124,130)(125,129)(126,128)(141,176)(142,182)(143,181)(144,180)(145,179)(146,178)(147,177)(148,204)(149,210)(150,209)(151,208)(152,207)(153,206)(154,205)(155,197)(156,203)(157,202)(158,201)(159,200)(160,199)(161,198)(162,190)(163,196)(164,195)(165,194)(166,193)(167,192)(168,191)(169,183)(170,189)(171,188)(172,187)(173,186)(174,185)(175,184)(211,316)(212,322)(213,321)(214,320)(215,319)(216,318)(217,317)(218,344)(219,350)(220,349)(221,348)(222,347)(223,346)(224,345)(225,337)(226,343)(227,342)(228,341)(229,340)(230,339)(231,338)(232,330)(233,336)(234,335)(235,334)(236,333)(237,332)(238,331)(239,323)(240,329)(241,328)(242,327)(243,326)(244,325)(245,324)(246,386)(247,392)(248,391)(249,390)(250,389)(251,388)(252,387)(253,414)(254,420)(255,419)(256,418)(257,417)(258,416)(259,415)(260,407)(261,413)(262,412)(263,411)(264,410)(265,409)(266,408)(267,400)(268,406)(269,405)(270,404)(271,403)(272,402)(273,401)(274,393)(275,399)(276,398)(277,397)(278,396)(279,395)(280,394)(281,351)(282,357)(283,356)(284,355)(285,354)(286,353)(287,352)(288,379)(289,385)(290,384)(291,383)(292,382)(293,381)(294,380)(295,372)(296,378)(297,377)(298,376)(299,375)(300,374)(301,373)(302,365)(303,371)(304,370)(305,369)(306,368)(307,367)(308,366)(309,358)(310,364)(311,363)(312,362)(313,361)(314,360)(315,359); s1 := Sym(420)!( 1,254)( 2,253)( 3,259)( 4,258)( 5,257)( 6,256)( 7,255)( 8,247)( 9,246)( 10,252)( 11,251)( 12,250)( 13,249)( 14,248)( 15,275)( 16,274)( 17,280)( 18,279)( 19,278)( 20,277)( 21,276)( 22,268)( 23,267)( 24,273)( 25,272)( 26,271)( 27,270)( 28,269)( 29,261)( 30,260)( 31,266)( 32,265)( 33,264)( 34,263)( 35,262)( 36,219)( 37,218)( 38,224)( 39,223)( 40,222)( 41,221)( 42,220)( 43,212)( 44,211)( 45,217)( 46,216)( 47,215)( 48,214)( 49,213)( 50,240)( 51,239)( 52,245)( 53,244)( 54,243)( 55,242)( 56,241)( 57,233)( 58,232)( 59,238)( 60,237)( 61,236)( 62,235)( 63,234)( 64,226)( 65,225)( 66,231)( 67,230)( 68,229)( 69,228)( 70,227)( 71,289)( 72,288)( 73,294)( 74,293)( 75,292)( 76,291)( 77,290)( 78,282)( 79,281)( 80,287)( 81,286)( 82,285)( 83,284)( 84,283)( 85,310)( 86,309)( 87,315)( 88,314)( 89,313)( 90,312)( 91,311)( 92,303)( 93,302)( 94,308)( 95,307)( 96,306)( 97,305)( 98,304)( 99,296)(100,295)(101,301)(102,300)(103,299)(104,298)(105,297)(106,359)(107,358)(108,364)(109,363)(110,362)(111,361)(112,360)(113,352)(114,351)(115,357)(116,356)(117,355)(118,354)(119,353)(120,380)(121,379)(122,385)(123,384)(124,383)(125,382)(126,381)(127,373)(128,372)(129,378)(130,377)(131,376)(132,375)(133,374)(134,366)(135,365)(136,371)(137,370)(138,369)(139,368)(140,367)(141,324)(142,323)(143,329)(144,328)(145,327)(146,326)(147,325)(148,317)(149,316)(150,322)(151,321)(152,320)(153,319)(154,318)(155,345)(156,344)(157,350)(158,349)(159,348)(160,347)(161,346)(162,338)(163,337)(164,343)(165,342)(166,341)(167,340)(168,339)(169,331)(170,330)(171,336)(172,335)(173,334)(174,333)(175,332)(176,394)(177,393)(178,399)(179,398)(180,397)(181,396)(182,395)(183,387)(184,386)(185,392)(186,391)(187,390)(188,389)(189,388)(190,415)(191,414)(192,420)(193,419)(194,418)(195,417)(196,416)(197,408)(198,407)(199,413)(200,412)(201,411)(202,410)(203,409)(204,401)(205,400)(206,406)(207,405)(208,404)(209,403)(210,402); poly := sub<Sym(420)|s0,s1>;
Finitely Presented Group Representation (Magma)
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*s0*s1 >;
References
None.
to this polytope.