Polytope of Type {20,10} with group SmallGroup(2000,372)

Overview

Group: SmallGroup(2000,372)
Rank: 3
Schläfli Type: {20,10}
Vertices, edges, …: 100, 500, 50
Order of s₀s₁s₂: 20
Order of s₀s₁s₂s₁: 10
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{10,10}*1000c

4-fold

{10,10}*500

5-fold

{20,10}*400a

10-fold

{10,10}*200a

25-fold

50-fold

100-fold

125-fold

{4,2}*16

250-fold

{2,2}*8

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s0*s1)^4> of order 5

18 facets

10 of {4}*8
8 of {20}*40

20 vertex figures

20 of {10}*20

P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2*s2> of order 5

10 facets

10 of {20}*40

36 vertex figures

16 of {10}*20
20 of {2}*4

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)(251,376)(252,380)(253,379)(254,378)(255,377)(256,396)(257,400)(258,399)(259,398)(260,397)(261,391)(262,395)(263,394)(264,393)(265,392)(266,386)(267,390)(268,389)(269,388)(270,387)(271,381)(272,385)(273,384)(274,383)(275,382)(276,401)(277,405)(278,404)(279,403)(280,402)(281,421)(282,425)(283,424)(284,423)(285,422)(286,416)(287,420)(288,419)(289,418)(290,417)(291,411)(292,415)(293,414)(294,413)(295,412)(296,406)(297,410)(298,409)(299,408)(300,407)(301,426)(302,430)(303,429)(304,428)(305,427)(306,446)(307,450)(308,449)(309,448)(310,447)(311,441)(312,445)(313,444)(314,443)(315,442)(316,436)(317,440)(318,439)(319,438)(320,437)(321,431)(322,435)(323,434)(324,433)(325,432)(326,451)(327,455)(328,454)(329,453)(330,452)(331,471)(332,475)(333,474)(334,473)(335,472)(336,466)(337,470)(338,469)(339,468)(340,467)(341,461)(342,465)(343,464)(344,463)(345,462)(346,456)(347,460)(348,459)(349,458)(350,457)(351,476)(352,480)(353,479)(354,478)(355,477)(356,496)(357,500)(358,499)(359,498)(360,497)(361,491)(362,495)(363,494)(364,493)(365,492)(366,486)(367,490)(368,489)(369,488)(370,487)(371,481)(372,485)(373,484)(374,483)(375,482);;
s1 := (  1,256)(  2,257)(  3,258)(  4,259)(  5,260)(  6,251)(  7,252)(  8,253)(  9,254)( 10,255)( 11,271)( 12,272)( 13,273)( 14,274)( 15,275)( 16,266)( 17,267)( 18,268)( 19,269)( 20,270)( 21,261)( 22,262)( 23,263)( 24,264)( 25,265)( 26,356)( 27,357)( 28,358)( 29,359)( 30,360)( 31,351)( 32,352)( 33,353)( 34,354)( 35,355)( 36,371)( 37,372)( 38,373)( 39,374)( 40,375)( 41,366)( 42,367)( 43,368)( 44,369)( 45,370)( 46,361)( 47,362)( 48,363)( 49,364)( 50,365)( 51,331)( 52,332)( 53,333)( 54,334)( 55,335)( 56,326)( 57,327)( 58,328)( 59,329)( 60,330)( 61,346)( 62,347)( 63,348)( 64,349)( 65,350)( 66,341)( 67,342)( 68,343)( 69,344)( 70,345)( 71,336)( 72,337)( 73,338)( 74,339)( 75,340)( 76,306)( 77,307)( 78,308)( 79,309)( 80,310)( 81,301)( 82,302)( 83,303)( 84,304)( 85,305)( 86,321)( 87,322)( 88,323)( 89,324)( 90,325)( 91,316)( 92,317)( 93,318)( 94,319)( 95,320)( 96,311)( 97,312)( 98,313)( 99,314)(100,315)(101,281)(102,282)(103,283)(104,284)(105,285)(106,276)(107,277)(108,278)(109,279)(110,280)(111,296)(112,297)(113,298)(114,299)(115,300)(116,291)(117,292)(118,293)(119,294)(120,295)(121,286)(122,287)(123,288)(124,289)(125,290)(126,381)(127,382)(128,383)(129,384)(130,385)(131,376)(132,377)(133,378)(134,379)(135,380)(136,396)(137,397)(138,398)(139,399)(140,400)(141,391)(142,392)(143,393)(144,394)(145,395)(146,386)(147,387)(148,388)(149,389)(150,390)(151,481)(152,482)(153,483)(154,484)(155,485)(156,476)(157,477)(158,478)(159,479)(160,480)(161,496)(162,497)(163,498)(164,499)(165,500)(166,491)(167,492)(168,493)(169,494)(170,495)(171,486)(172,487)(173,488)(174,489)(175,490)(176,456)(177,457)(178,458)(179,459)(180,460)(181,451)(182,452)(183,453)(184,454)(185,455)(186,471)(187,472)(188,473)(189,474)(190,475)(191,466)(192,467)(193,468)(194,469)(195,470)(196,461)(197,462)(198,463)(199,464)(200,465)(201,431)(202,432)(203,433)(204,434)(205,435)(206,426)(207,427)(208,428)(209,429)(210,430)(211,446)(212,447)(213,448)(214,449)(215,450)(216,441)(217,442)(218,443)(219,444)(220,445)(221,436)(222,437)(223,438)(224,439)(225,440)(226,406)(227,407)(228,408)(229,409)(230,410)(231,401)(232,402)(233,403)(234,404)(235,405)(236,421)(237,422)(238,423)(239,424)(240,425)(241,416)(242,417)(243,418)(244,419)(245,420)(246,411)(247,412)(248,413)(249,414)(250,415);;
s2 := (  1, 26)(  2, 30)(  3, 29)(  4, 28)(  5, 27)(  6, 32)(  7, 31)(  8, 35)(  9, 34)( 10, 33)( 11, 38)( 12, 37)( 13, 36)( 14, 40)( 15, 39)( 16, 44)( 17, 43)( 18, 42)( 19, 41)( 20, 45)( 21, 50)( 22, 49)( 23, 48)( 24, 47)( 25, 46)( 51,101)( 52,105)( 53,104)( 54,103)( 55,102)( 56,107)( 57,106)( 58,110)( 59,109)( 60,108)( 61,113)( 62,112)( 63,111)( 64,115)( 65,114)( 66,119)( 67,118)( 68,117)( 69,116)( 70,120)( 71,125)( 72,124)( 73,123)( 74,122)( 75,121)( 77, 80)( 78, 79)( 81, 82)( 83, 85)( 86, 88)( 89, 90)( 91, 94)( 92, 93)( 96,100)( 97, 99)(126,151)(127,155)(128,154)(129,153)(130,152)(131,157)(132,156)(133,160)(134,159)(135,158)(136,163)(137,162)(138,161)(139,165)(140,164)(141,169)(142,168)(143,167)(144,166)(145,170)(146,175)(147,174)(148,173)(149,172)(150,171)(176,226)(177,230)(178,229)(179,228)(180,227)(181,232)(182,231)(183,235)(184,234)(185,233)(186,238)(187,237)(188,236)(189,240)(190,239)(191,244)(192,243)(193,242)(194,241)(195,245)(196,250)(197,249)(198,248)(199,247)(200,246)(202,205)(203,204)(206,207)(208,210)(211,213)(214,215)(216,219)(217,218)(221,225)(222,224)(251,276)(252,280)(253,279)(254,278)(255,277)(256,282)(257,281)(258,285)(259,284)(260,283)(261,288)(262,287)(263,286)(264,290)(265,289)(266,294)(267,293)(268,292)(269,291)(270,295)(271,300)(272,299)(273,298)(274,297)(275,296)(301,351)(302,355)(303,354)(304,353)(305,352)(306,357)(307,356)(308,360)(309,359)(310,358)(311,363)(312,362)(313,361)(314,365)(315,364)(316,369)(317,368)(318,367)(319,366)(320,370)(321,375)(322,374)(323,373)(324,372)(325,371)(327,330)(328,329)(331,332)(333,335)(336,338)(339,340)(341,344)(342,343)(346,350)(347,349)(376,401)(377,405)(378,404)(379,403)(380,402)(381,407)(382,406)(383,410)(384,409)(385,408)(386,413)(387,412)(388,411)(389,415)(390,414)(391,419)(392,418)(393,417)(394,416)(395,420)(396,425)(397,424)(398,423)(399,422)(400,421)(426,476)(427,480)(428,479)(429,478)(430,477)(431,482)(432,481)(433,485)(434,484)(435,483)(436,488)(437,487)(438,486)(439,490)(440,489)(441,494)(442,493)(443,492)(444,491)(445,495)(446,500)(447,499)(448,498)(449,497)(450,496)(452,455)(453,454)(456,457)(458,460)(461,463)(464,465)(466,469)(467,468)(471,475)(472,474);;
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*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*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(500)!(  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)(251,376)(252,380)(253,379)(254,378)(255,377)(256,396)(257,400)(258,399)(259,398)(260,397)(261,391)(262,395)(263,394)(264,393)(265,392)(266,386)(267,390)(268,389)(269,388)(270,387)(271,381)(272,385)(273,384)(274,383)(275,382)(276,401)(277,405)(278,404)(279,403)(280,402)(281,421)(282,425)(283,424)(284,423)(285,422)(286,416)(287,420)(288,419)(289,418)(290,417)(291,411)(292,415)(293,414)(294,413)(295,412)(296,406)(297,410)(298,409)(299,408)(300,407)(301,426)(302,430)(303,429)(304,428)(305,427)(306,446)(307,450)(308,449)(309,448)(310,447)(311,441)(312,445)(313,444)(314,443)(315,442)(316,436)(317,440)(318,439)(319,438)(320,437)(321,431)(322,435)(323,434)(324,433)(325,432)(326,451)(327,455)(328,454)(329,453)(330,452)(331,471)(332,475)(333,474)(334,473)(335,472)(336,466)(337,470)(338,469)(339,468)(340,467)(341,461)(342,465)(343,464)(344,463)(345,462)(346,456)(347,460)(348,459)(349,458)(350,457)(351,476)(352,480)(353,479)(354,478)(355,477)(356,496)(357,500)(358,499)(359,498)(360,497)(361,491)(362,495)(363,494)(364,493)(365,492)(366,486)(367,490)(368,489)(369,488)(370,487)(371,481)(372,485)(373,484)(374,483)(375,482);
s1 := Sym(500)!(  1,256)(  2,257)(  3,258)(  4,259)(  5,260)(  6,251)(  7,252)(  8,253)(  9,254)( 10,255)( 11,271)( 12,272)( 13,273)( 14,274)( 15,275)( 16,266)( 17,267)( 18,268)( 19,269)( 20,270)( 21,261)( 22,262)( 23,263)( 24,264)( 25,265)( 26,356)( 27,357)( 28,358)( 29,359)( 30,360)( 31,351)( 32,352)( 33,353)( 34,354)( 35,355)( 36,371)( 37,372)( 38,373)( 39,374)( 40,375)( 41,366)( 42,367)( 43,368)( 44,369)( 45,370)( 46,361)( 47,362)( 48,363)( 49,364)( 50,365)( 51,331)( 52,332)( 53,333)( 54,334)( 55,335)( 56,326)( 57,327)( 58,328)( 59,329)( 60,330)( 61,346)( 62,347)( 63,348)( 64,349)( 65,350)( 66,341)( 67,342)( 68,343)( 69,344)( 70,345)( 71,336)( 72,337)( 73,338)( 74,339)( 75,340)( 76,306)( 77,307)( 78,308)( 79,309)( 80,310)( 81,301)( 82,302)( 83,303)( 84,304)( 85,305)( 86,321)( 87,322)( 88,323)( 89,324)( 90,325)( 91,316)( 92,317)( 93,318)( 94,319)( 95,320)( 96,311)( 97,312)( 98,313)( 99,314)(100,315)(101,281)(102,282)(103,283)(104,284)(105,285)(106,276)(107,277)(108,278)(109,279)(110,280)(111,296)(112,297)(113,298)(114,299)(115,300)(116,291)(117,292)(118,293)(119,294)(120,295)(121,286)(122,287)(123,288)(124,289)(125,290)(126,381)(127,382)(128,383)(129,384)(130,385)(131,376)(132,377)(133,378)(134,379)(135,380)(136,396)(137,397)(138,398)(139,399)(140,400)(141,391)(142,392)(143,393)(144,394)(145,395)(146,386)(147,387)(148,388)(149,389)(150,390)(151,481)(152,482)(153,483)(154,484)(155,485)(156,476)(157,477)(158,478)(159,479)(160,480)(161,496)(162,497)(163,498)(164,499)(165,500)(166,491)(167,492)(168,493)(169,494)(170,495)(171,486)(172,487)(173,488)(174,489)(175,490)(176,456)(177,457)(178,458)(179,459)(180,460)(181,451)(182,452)(183,453)(184,454)(185,455)(186,471)(187,472)(188,473)(189,474)(190,475)(191,466)(192,467)(193,468)(194,469)(195,470)(196,461)(197,462)(198,463)(199,464)(200,465)(201,431)(202,432)(203,433)(204,434)(205,435)(206,426)(207,427)(208,428)(209,429)(210,430)(211,446)(212,447)(213,448)(214,449)(215,450)(216,441)(217,442)(218,443)(219,444)(220,445)(221,436)(222,437)(223,438)(224,439)(225,440)(226,406)(227,407)(228,408)(229,409)(230,410)(231,401)(232,402)(233,403)(234,404)(235,405)(236,421)(237,422)(238,423)(239,424)(240,425)(241,416)(242,417)(243,418)(244,419)(245,420)(246,411)(247,412)(248,413)(249,414)(250,415);
s2 := Sym(500)!(  1, 26)(  2, 30)(  3, 29)(  4, 28)(  5, 27)(  6, 32)(  7, 31)(  8, 35)(  9, 34)( 10, 33)( 11, 38)( 12, 37)( 13, 36)( 14, 40)( 15, 39)( 16, 44)( 17, 43)( 18, 42)( 19, 41)( 20, 45)( 21, 50)( 22, 49)( 23, 48)( 24, 47)( 25, 46)( 51,101)( 52,105)( 53,104)( 54,103)( 55,102)( 56,107)( 57,106)( 58,110)( 59,109)( 60,108)( 61,113)( 62,112)( 63,111)( 64,115)( 65,114)( 66,119)( 67,118)( 68,117)( 69,116)( 70,120)( 71,125)( 72,124)( 73,123)( 74,122)( 75,121)( 77, 80)( 78, 79)( 81, 82)( 83, 85)( 86, 88)( 89, 90)( 91, 94)( 92, 93)( 96,100)( 97, 99)(126,151)(127,155)(128,154)(129,153)(130,152)(131,157)(132,156)(133,160)(134,159)(135,158)(136,163)(137,162)(138,161)(139,165)(140,164)(141,169)(142,168)(143,167)(144,166)(145,170)(146,175)(147,174)(148,173)(149,172)(150,171)(176,226)(177,230)(178,229)(179,228)(180,227)(181,232)(182,231)(183,235)(184,234)(185,233)(186,238)(187,237)(188,236)(189,240)(190,239)(191,244)(192,243)(193,242)(194,241)(195,245)(196,250)(197,249)(198,248)(199,247)(200,246)(202,205)(203,204)(206,207)(208,210)(211,213)(214,215)(216,219)(217,218)(221,225)(222,224)(251,276)(252,280)(253,279)(254,278)(255,277)(256,282)(257,281)(258,285)(259,284)(260,283)(261,288)(262,287)(263,286)(264,290)(265,289)(266,294)(267,293)(268,292)(269,291)(270,295)(271,300)(272,299)(273,298)(274,297)(275,296)(301,351)(302,355)(303,354)(304,353)(305,352)(306,357)(307,356)(308,360)(309,359)(310,358)(311,363)(312,362)(313,361)(314,365)(315,364)(316,369)(317,368)(318,367)(319,366)(320,370)(321,375)(322,374)(323,373)(324,372)(325,371)(327,330)(328,329)(331,332)(333,335)(336,338)(339,340)(341,344)(342,343)(346,350)(347,349)(376,401)(377,405)(378,404)(379,403)(380,402)(381,407)(382,406)(383,410)(384,409)(385,408)(386,413)(387,412)(388,411)(389,415)(390,414)(391,419)(392,418)(393,417)(394,416)(395,420)(396,425)(397,424)(398,423)(399,422)(400,421)(426,476)(427,480)(428,479)(429,478)(430,477)(431,482)(432,481)(433,485)(434,484)(435,483)(436,488)(437,487)(438,486)(439,490)(440,489)(441,494)(442,493)(443,492)(444,491)(445,495)(446,500)(447,499)(448,498)(449,497)(450,496)(452,455)(453,454)(456,457)(458,460)(461,463)(464,465)(466,469)(467,468)(471,475)(472,474);
poly := sub<Sym(500)|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*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References

None.

to this polytope.