Overview
- Group
- SmallGroup(1600,3558)
- Rank
- 3
- Schläfli Type
- {10,80}
- Vertices, edges, …
- 10, 400, 80
- Order of s0s1s2
- 80
- Order of s0s1s2s1
- 10
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
5-fold
8-fold
10-fold
16-fold
20-fold
25-fold
40-fold
50-fold
80-fold
100-fold
200-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, 5)( 3, 4)( 6, 21)( 7, 25)( 8, 24)( 9, 23)( 10, 22)( 11, 16)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 27, 30)( 28, 29)( 31, 46)( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 52, 55)( 53, 54)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)( 61, 66)( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 77, 80)( 78, 79)( 81, 96)( 82,100)( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)( 89, 93)( 90, 92)(102,105)(103,104)(106,121)(107,125)(108,124)(109,123)(110,122)(111,116)(112,120)(113,119)(114,118)(115,117)(127,130)(128,129)(131,146)(132,150)(133,149)(134,148)(135,147)(136,141)(137,145)(138,144)(139,143)(140,142)(152,155)(153,154)(156,171)(157,175)(158,174)(159,173)(160,172)(161,166)(162,170)(163,169)(164,168)(165,167)(177,180)(178,179)(181,196)(182,200)(183,199)(184,198)(185,197)(186,191)(187,195)(188,194)(189,193)(190,192)(202,205)(203,204)(206,221)(207,225)(208,224)(209,223)(210,222)(211,216)(212,220)(213,219)(214,218)(215,217)(227,230)(228,229)(231,246)(232,250)(233,249)(234,248)(235,247)(236,241)(237,245)(238,244)(239,243)(240,242)(252,255)(253,254)(256,271)(257,275)(258,274)(259,273)(260,272)(261,266)(262,270)(263,269)(264,268)(265,267)(277,280)(278,279)(281,296)(282,300)(283,299)(284,298)(285,297)(286,291)(287,295)(288,294)(289,293)(290,292)(302,305)(303,304)(306,321)(307,325)(308,324)(309,323)(310,322)(311,316)(312,320)(313,319)(314,318)(315,317)(327,330)(328,329)(331,346)(332,350)(333,349)(334,348)(335,347)(336,341)(337,345)(338,344)(339,343)(340,342)(352,355)(353,354)(356,371)(357,375)(358,374)(359,373)(360,372)(361,366)(362,370)(363,369)(364,368)(365,367)(377,380)(378,379)(381,396)(382,400)(383,399)(384,398)(385,397)(386,391)(387,395)(388,394)(389,393)(390,392);; s1 := ( 1,207)( 2,206)( 3,210)( 4,209)( 5,208)( 6,202)( 7,201)( 8,205)( 9,204)( 10,203)( 11,222)( 12,221)( 13,225)( 14,224)( 15,223)( 16,217)( 17,216)( 18,220)( 19,219)( 20,218)( 21,212)( 22,211)( 23,215)( 24,214)( 25,213)( 26,232)( 27,231)( 28,235)( 29,234)( 30,233)( 31,227)( 32,226)( 33,230)( 34,229)( 35,228)( 36,247)( 37,246)( 38,250)( 39,249)( 40,248)( 41,242)( 42,241)( 43,245)( 44,244)( 45,243)( 46,237)( 47,236)( 48,240)( 49,239)( 50,238)( 51,282)( 52,281)( 53,285)( 54,284)( 55,283)( 56,277)( 57,276)( 58,280)( 59,279)( 60,278)( 61,297)( 62,296)( 63,300)( 64,299)( 65,298)( 66,292)( 67,291)( 68,295)( 69,294)( 70,293)( 71,287)( 72,286)( 73,290)( 74,289)( 75,288)( 76,257)( 77,256)( 78,260)( 79,259)( 80,258)( 81,252)( 82,251)( 83,255)( 84,254)( 85,253)( 86,272)( 87,271)( 88,275)( 89,274)( 90,273)( 91,267)( 92,266)( 93,270)( 94,269)( 95,268)( 96,262)( 97,261)( 98,265)( 99,264)(100,263)(101,357)(102,356)(103,360)(104,359)(105,358)(106,352)(107,351)(108,355)(109,354)(110,353)(111,372)(112,371)(113,375)(114,374)(115,373)(116,367)(117,366)(118,370)(119,369)(120,368)(121,362)(122,361)(123,365)(124,364)(125,363)(126,382)(127,381)(128,385)(129,384)(130,383)(131,377)(132,376)(133,380)(134,379)(135,378)(136,397)(137,396)(138,400)(139,399)(140,398)(141,392)(142,391)(143,395)(144,394)(145,393)(146,387)(147,386)(148,390)(149,389)(150,388)(151,307)(152,306)(153,310)(154,309)(155,308)(156,302)(157,301)(158,305)(159,304)(160,303)(161,322)(162,321)(163,325)(164,324)(165,323)(166,317)(167,316)(168,320)(169,319)(170,318)(171,312)(172,311)(173,315)(174,314)(175,313)(176,332)(177,331)(178,335)(179,334)(180,333)(181,327)(182,326)(183,330)(184,329)(185,328)(186,347)(187,346)(188,350)(189,349)(190,348)(191,342)(192,341)(193,345)(194,344)(195,343)(196,337)(197,336)(198,340)(199,339)(200,338);; s2 := ( 6, 21)( 7, 22)( 8, 23)( 9, 24)( 10, 25)( 11, 16)( 12, 17)( 13, 18)( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 51, 76)( 52, 77)( 53, 78)( 54, 79)( 55, 80)( 56, 96)( 57, 97)( 58, 98)( 59, 99)( 60,100)( 61, 91)( 62, 92)( 63, 93)( 64, 94)( 65, 95)( 66, 86)( 67, 87)( 68, 88)( 69, 89)( 70, 90)( 71, 81)( 72, 82)( 73, 83)( 74, 84)( 75, 85)(101,151)(102,152)(103,153)(104,154)(105,155)(106,171)(107,172)(108,173)(109,174)(110,175)(111,166)(112,167)(113,168)(114,169)(115,170)(116,161)(117,162)(118,163)(119,164)(120,165)(121,156)(122,157)(123,158)(124,159)(125,160)(126,176)(127,177)(128,178)(129,179)(130,180)(131,196)(132,197)(133,198)(134,199)(135,200)(136,191)(137,192)(138,193)(139,194)(140,195)(141,186)(142,187)(143,188)(144,189)(145,190)(146,181)(147,182)(148,183)(149,184)(150,185)(201,301)(202,302)(203,303)(204,304)(205,305)(206,321)(207,322)(208,323)(209,324)(210,325)(211,316)(212,317)(213,318)(214,319)(215,320)(216,311)(217,312)(218,313)(219,314)(220,315)(221,306)(222,307)(223,308)(224,309)(225,310)(226,326)(227,327)(228,328)(229,329)(230,330)(231,346)(232,347)(233,348)(234,349)(235,350)(236,341)(237,342)(238,343)(239,344)(240,345)(241,336)(242,337)(243,338)(244,339)(245,340)(246,331)(247,332)(248,333)(249,334)(250,335)(251,376)(252,377)(253,378)(254,379)(255,380)(256,396)(257,397)(258,398)(259,399)(260,400)(261,391)(262,392)(263,393)(264,394)(265,395)(266,386)(267,387)(268,388)(269,389)(270,390)(271,381)(272,382)(273,383)(274,384)(275,385)(276,351)(277,352)(278,353)(279,354)(280,355)(281,371)(282,372)(283,373)(284,374)(285,375)(286,366)(287,367)(288,368)(289,369)(290,370)(291,361)(292,362)(293,363)(294,364)(295,365)(296,356)(297,357)(298,358)(299,359)(300,360);; poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(400)!( 2, 5)( 3, 4)( 6, 21)( 7, 25)( 8, 24)( 9, 23)( 10, 22)( 11, 16)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 27, 30)( 28, 29)( 31, 46)( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 52, 55)( 53, 54)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)( 61, 66)( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 77, 80)( 78, 79)( 81, 96)( 82,100)( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)( 89, 93)( 90, 92)(102,105)(103,104)(106,121)(107,125)(108,124)(109,123)(110,122)(111,116)(112,120)(113,119)(114,118)(115,117)(127,130)(128,129)(131,146)(132,150)(133,149)(134,148)(135,147)(136,141)(137,145)(138,144)(139,143)(140,142)(152,155)(153,154)(156,171)(157,175)(158,174)(159,173)(160,172)(161,166)(162,170)(163,169)(164,168)(165,167)(177,180)(178,179)(181,196)(182,200)(183,199)(184,198)(185,197)(186,191)(187,195)(188,194)(189,193)(190,192)(202,205)(203,204)(206,221)(207,225)(208,224)(209,223)(210,222)(211,216)(212,220)(213,219)(214,218)(215,217)(227,230)(228,229)(231,246)(232,250)(233,249)(234,248)(235,247)(236,241)(237,245)(238,244)(239,243)(240,242)(252,255)(253,254)(256,271)(257,275)(258,274)(259,273)(260,272)(261,266)(262,270)(263,269)(264,268)(265,267)(277,280)(278,279)(281,296)(282,300)(283,299)(284,298)(285,297)(286,291)(287,295)(288,294)(289,293)(290,292)(302,305)(303,304)(306,321)(307,325)(308,324)(309,323)(310,322)(311,316)(312,320)(313,319)(314,318)(315,317)(327,330)(328,329)(331,346)(332,350)(333,349)(334,348)(335,347)(336,341)(337,345)(338,344)(339,343)(340,342)(352,355)(353,354)(356,371)(357,375)(358,374)(359,373)(360,372)(361,366)(362,370)(363,369)(364,368)(365,367)(377,380)(378,379)(381,396)(382,400)(383,399)(384,398)(385,397)(386,391)(387,395)(388,394)(389,393)(390,392); s1 := Sym(400)!( 1,207)( 2,206)( 3,210)( 4,209)( 5,208)( 6,202)( 7,201)( 8,205)( 9,204)( 10,203)( 11,222)( 12,221)( 13,225)( 14,224)( 15,223)( 16,217)( 17,216)( 18,220)( 19,219)( 20,218)( 21,212)( 22,211)( 23,215)( 24,214)( 25,213)( 26,232)( 27,231)( 28,235)( 29,234)( 30,233)( 31,227)( 32,226)( 33,230)( 34,229)( 35,228)( 36,247)( 37,246)( 38,250)( 39,249)( 40,248)( 41,242)( 42,241)( 43,245)( 44,244)( 45,243)( 46,237)( 47,236)( 48,240)( 49,239)( 50,238)( 51,282)( 52,281)( 53,285)( 54,284)( 55,283)( 56,277)( 57,276)( 58,280)( 59,279)( 60,278)( 61,297)( 62,296)( 63,300)( 64,299)( 65,298)( 66,292)( 67,291)( 68,295)( 69,294)( 70,293)( 71,287)( 72,286)( 73,290)( 74,289)( 75,288)( 76,257)( 77,256)( 78,260)( 79,259)( 80,258)( 81,252)( 82,251)( 83,255)( 84,254)( 85,253)( 86,272)( 87,271)( 88,275)( 89,274)( 90,273)( 91,267)( 92,266)( 93,270)( 94,269)( 95,268)( 96,262)( 97,261)( 98,265)( 99,264)(100,263)(101,357)(102,356)(103,360)(104,359)(105,358)(106,352)(107,351)(108,355)(109,354)(110,353)(111,372)(112,371)(113,375)(114,374)(115,373)(116,367)(117,366)(118,370)(119,369)(120,368)(121,362)(122,361)(123,365)(124,364)(125,363)(126,382)(127,381)(128,385)(129,384)(130,383)(131,377)(132,376)(133,380)(134,379)(135,378)(136,397)(137,396)(138,400)(139,399)(140,398)(141,392)(142,391)(143,395)(144,394)(145,393)(146,387)(147,386)(148,390)(149,389)(150,388)(151,307)(152,306)(153,310)(154,309)(155,308)(156,302)(157,301)(158,305)(159,304)(160,303)(161,322)(162,321)(163,325)(164,324)(165,323)(166,317)(167,316)(168,320)(169,319)(170,318)(171,312)(172,311)(173,315)(174,314)(175,313)(176,332)(177,331)(178,335)(179,334)(180,333)(181,327)(182,326)(183,330)(184,329)(185,328)(186,347)(187,346)(188,350)(189,349)(190,348)(191,342)(192,341)(193,345)(194,344)(195,343)(196,337)(197,336)(198,340)(199,339)(200,338); s2 := Sym(400)!( 6, 21)( 7, 22)( 8, 23)( 9, 24)( 10, 25)( 11, 16)( 12, 17)( 13, 18)( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 51, 76)( 52, 77)( 53, 78)( 54, 79)( 55, 80)( 56, 96)( 57, 97)( 58, 98)( 59, 99)( 60,100)( 61, 91)( 62, 92)( 63, 93)( 64, 94)( 65, 95)( 66, 86)( 67, 87)( 68, 88)( 69, 89)( 70, 90)( 71, 81)( 72, 82)( 73, 83)( 74, 84)( 75, 85)(101,151)(102,152)(103,153)(104,154)(105,155)(106,171)(107,172)(108,173)(109,174)(110,175)(111,166)(112,167)(113,168)(114,169)(115,170)(116,161)(117,162)(118,163)(119,164)(120,165)(121,156)(122,157)(123,158)(124,159)(125,160)(126,176)(127,177)(128,178)(129,179)(130,180)(131,196)(132,197)(133,198)(134,199)(135,200)(136,191)(137,192)(138,193)(139,194)(140,195)(141,186)(142,187)(143,188)(144,189)(145,190)(146,181)(147,182)(148,183)(149,184)(150,185)(201,301)(202,302)(203,303)(204,304)(205,305)(206,321)(207,322)(208,323)(209,324)(210,325)(211,316)(212,317)(213,318)(214,319)(215,320)(216,311)(217,312)(218,313)(219,314)(220,315)(221,306)(222,307)(223,308)(224,309)(225,310)(226,326)(227,327)(228,328)(229,329)(230,330)(231,346)(232,347)(233,348)(234,349)(235,350)(236,341)(237,342)(238,343)(239,344)(240,345)(241,336)(242,337)(243,338)(244,339)(245,340)(246,331)(247,332)(248,333)(249,334)(250,335)(251,376)(252,377)(253,378)(254,379)(255,380)(256,396)(257,397)(258,398)(259,399)(260,400)(261,391)(262,392)(263,393)(264,394)(265,395)(266,386)(267,387)(268,388)(269,389)(270,390)(271,381)(272,382)(273,383)(274,384)(275,385)(276,351)(277,352)(278,353)(279,354)(280,355)(281,371)(282,372)(283,373)(284,374)(285,375)(286,366)(287,367)(288,368)(289,369)(290,370)(291,361)(292,362)(293,363)(294,364)(295,365)(296,356)(297,357)(298,358)(299,359)(300,360); poly := sub<Sym(400)|s0,s1,s2>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1 >;
References
None.
to this polytope.