Polytope of Type {4,100}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,100}*1600
if this polytope has a name.
Group : SmallGroup(1600,368)
Rank : 3
Schlafli Type : {4,100}
Number of vertices, edges, etc : 8, 400, 200
Order of s₀s₁s₂ : 100
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {4,100}*800
   4-fold quotients : {2,100}*400, {4,50}*400
   5-fold quotients : {4,20}*320
   8-fold quotients : {2,50}*200
   10-fold quotients : {4,20}*160
   16-fold quotients : {2,25}*100
   20-fold quotients : {2,20}*80, {4,10}*80
   25-fold quotients : {4,4}*64
   40-fold quotients : {2,10}*40
   50-fold quotients : {4,4}*32
   80-fold quotients : {2,5}*20
   100-fold quotients : {2,4}*16, {4,2}*16
   200-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 51, 76)( 52, 77)( 53, 78)( 54, 79)( 55, 80)( 56, 81)( 57, 82)( 58, 83)
( 59, 84)( 60, 85)( 61, 86)( 62, 87)( 63, 88)( 64, 89)( 65, 90)( 66, 91)
( 67, 92)( 68, 93)( 69, 94)( 70, 95)( 71, 96)( 72, 97)( 73, 98)( 74, 99)
( 75,100)(151,176)(152,177)(153,178)(154,179)(155,180)(156,181)(157,182)
(158,183)(159,184)(160,185)(161,186)(162,187)(163,188)(164,189)(165,190)
(166,191)(167,192)(168,193)(169,194)(170,195)(171,196)(172,197)(173,198)
(174,199)(175,200)(201,301)(202,302)(203,303)(204,304)(205,305)(206,306)
(207,307)(208,308)(209,309)(210,310)(211,311)(212,312)(213,313)(214,314)
(215,315)(216,316)(217,317)(218,318)(219,319)(220,320)(221,321)(222,322)
(223,323)(224,324)(225,325)(226,326)(227,327)(228,328)(229,329)(230,330)
(231,331)(232,332)(233,333)(234,334)(235,335)(236,336)(237,337)(238,338)
(239,339)(240,340)(241,341)(242,342)(243,343)(244,344)(245,345)(246,346)
(247,347)(248,348)(249,349)(250,350)(251,376)(252,377)(253,378)(254,379)
(255,380)(256,381)(257,382)(258,383)(259,384)(260,385)(261,386)(262,387)
(263,388)(264,389)(265,390)(266,391)(267,392)(268,393)(269,394)(270,395)
(271,396)(272,397)(273,398)(274,399)(275,400)(276,351)(277,352)(278,353)
(279,354)(280,355)(281,356)(282,357)(283,358)(284,359)(285,360)(286,361)
(287,362)(288,363)(289,364)(290,365)(291,366)(292,367)(293,368)(294,369)
(295,370)(296,371)(297,372)(298,373)(299,374)(300,375);;
s1 := (  1,201)(  2,205)(  3,204)(  4,203)(  5,202)(  6,225)(  7,224)(  8,223)
(  9,222)( 10,221)( 11,220)( 12,219)( 13,218)( 14,217)( 15,216)( 16,215)
( 17,214)( 18,213)( 19,212)( 20,211)( 21,210)( 22,209)( 23,208)( 24,207)
( 25,206)( 26,226)( 27,230)( 28,229)( 29,228)( 30,227)( 31,250)( 32,249)
( 33,248)( 34,247)( 35,246)( 36,245)( 37,244)( 38,243)( 39,242)( 40,241)
( 41,240)( 42,239)( 43,238)( 44,237)( 45,236)( 46,235)( 47,234)( 48,233)
( 49,232)( 50,231)( 51,251)( 52,255)( 53,254)( 54,253)( 55,252)( 56,275)
( 57,274)( 58,273)( 59,272)( 60,271)( 61,270)( 62,269)( 63,268)( 64,267)
( 65,266)( 66,265)( 67,264)( 68,263)( 69,262)( 70,261)( 71,260)( 72,259)
( 73,258)( 74,257)( 75,256)( 76,276)( 77,280)( 78,279)( 79,278)( 80,277)
( 81,300)( 82,299)( 83,298)( 84,297)( 85,296)( 86,295)( 87,294)( 88,293)
( 89,292)( 90,291)( 91,290)( 92,289)( 93,288)( 94,287)( 95,286)( 96,285)
( 97,284)( 98,283)( 99,282)(100,281)(101,301)(102,305)(103,304)(104,303)
(105,302)(106,325)(107,324)(108,323)(109,322)(110,321)(111,320)(112,319)
(113,318)(114,317)(115,316)(116,315)(117,314)(118,313)(119,312)(120,311)
(121,310)(122,309)(123,308)(124,307)(125,306)(126,326)(127,330)(128,329)
(129,328)(130,327)(131,350)(132,349)(133,348)(134,347)(135,346)(136,345)
(137,344)(138,343)(139,342)(140,341)(141,340)(142,339)(143,338)(144,337)
(145,336)(146,335)(147,334)(148,333)(149,332)(150,331)(151,351)(152,355)
(153,354)(154,353)(155,352)(156,375)(157,374)(158,373)(159,372)(160,371)
(161,370)(162,369)(163,368)(164,367)(165,366)(166,365)(167,364)(168,363)
(169,362)(170,361)(171,360)(172,359)(173,358)(174,357)(175,356)(176,376)
(177,380)(178,379)(179,378)(180,377)(181,400)(182,399)(183,398)(184,397)
(185,396)(186,395)(187,394)(188,393)(189,392)(190,391)(191,390)(192,389)
(193,388)(194,387)(195,386)(196,385)(197,384)(198,383)(199,382)(200,381);;
s2 := (  1,  6)(  2, 10)(  3,  9)(  4,  8)(  5,  7)( 11, 25)( 12, 24)( 13, 23)
( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 26, 31)( 27, 35)( 28, 34)( 29, 33)
( 30, 32)( 36, 50)( 37, 49)( 38, 48)( 39, 47)( 40, 46)( 41, 45)( 42, 44)
( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 75)( 62, 74)( 63, 73)
( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 76, 81)( 77, 85)( 78, 84)( 79, 83)
( 80, 82)( 86,100)( 87, 99)( 88, 98)( 89, 97)( 90, 96)( 91, 95)( 92, 94)
(101,131)(102,135)(103,134)(104,133)(105,132)(106,126)(107,130)(108,129)
(109,128)(110,127)(111,150)(112,149)(113,148)(114,147)(115,146)(116,145)
(117,144)(118,143)(119,142)(120,141)(121,140)(122,139)(123,138)(124,137)
(125,136)(151,181)(152,185)(153,184)(154,183)(155,182)(156,176)(157,180)
(158,179)(159,178)(160,177)(161,200)(162,199)(163,198)(164,197)(165,196)
(166,195)(167,194)(168,193)(169,192)(170,191)(171,190)(172,189)(173,188)
(174,187)(175,186)(201,256)(202,260)(203,259)(204,258)(205,257)(206,251)
(207,255)(208,254)(209,253)(210,252)(211,275)(212,274)(213,273)(214,272)
(215,271)(216,270)(217,269)(218,268)(219,267)(220,266)(221,265)(222,264)
(223,263)(224,262)(225,261)(226,281)(227,285)(228,284)(229,283)(230,282)
(231,276)(232,280)(233,279)(234,278)(235,277)(236,300)(237,299)(238,298)
(239,297)(240,296)(241,295)(242,294)(243,293)(244,292)(245,291)(246,290)
(247,289)(248,288)(249,287)(250,286)(301,381)(302,385)(303,384)(304,383)
(305,382)(306,376)(307,380)(308,379)(309,378)(310,377)(311,400)(312,399)
(313,398)(314,397)(315,396)(316,395)(317,394)(318,393)(319,392)(320,391)
(321,390)(322,389)(323,388)(324,387)(325,386)(326,356)(327,360)(328,359)
(329,358)(330,357)(331,351)(332,355)(333,354)(334,353)(335,352)(336,375)
(337,374)(338,373)(339,372)(340,371)(341,370)(342,369)(343,368)(344,367)
(345,366)(346,365)(347,364)(348,363)(349,362)(350,361);;
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*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s0*s2*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(400)!( 51, 76)( 52, 77)( 53, 78)( 54, 79)( 55, 80)( 56, 81)( 57, 82)
( 58, 83)( 59, 84)( 60, 85)( 61, 86)( 62, 87)( 63, 88)( 64, 89)( 65, 90)
( 66, 91)( 67, 92)( 68, 93)( 69, 94)( 70, 95)( 71, 96)( 72, 97)( 73, 98)
( 74, 99)( 75,100)(151,176)(152,177)(153,178)(154,179)(155,180)(156,181)
(157,182)(158,183)(159,184)(160,185)(161,186)(162,187)(163,188)(164,189)
(165,190)(166,191)(167,192)(168,193)(169,194)(170,195)(171,196)(172,197)
(173,198)(174,199)(175,200)(201,301)(202,302)(203,303)(204,304)(205,305)
(206,306)(207,307)(208,308)(209,309)(210,310)(211,311)(212,312)(213,313)
(214,314)(215,315)(216,316)(217,317)(218,318)(219,319)(220,320)(221,321)
(222,322)(223,323)(224,324)(225,325)(226,326)(227,327)(228,328)(229,329)
(230,330)(231,331)(232,332)(233,333)(234,334)(235,335)(236,336)(237,337)
(238,338)(239,339)(240,340)(241,341)(242,342)(243,343)(244,344)(245,345)
(246,346)(247,347)(248,348)(249,349)(250,350)(251,376)(252,377)(253,378)
(254,379)(255,380)(256,381)(257,382)(258,383)(259,384)(260,385)(261,386)
(262,387)(263,388)(264,389)(265,390)(266,391)(267,392)(268,393)(269,394)
(270,395)(271,396)(272,397)(273,398)(274,399)(275,400)(276,351)(277,352)
(278,353)(279,354)(280,355)(281,356)(282,357)(283,358)(284,359)(285,360)
(286,361)(287,362)(288,363)(289,364)(290,365)(291,366)(292,367)(293,368)
(294,369)(295,370)(296,371)(297,372)(298,373)(299,374)(300,375);
s1 := Sym(400)!(  1,201)(  2,205)(  3,204)(  4,203)(  5,202)(  6,225)(  7,224)
(  8,223)(  9,222)( 10,221)( 11,220)( 12,219)( 13,218)( 14,217)( 15,216)
( 16,215)( 17,214)( 18,213)( 19,212)( 20,211)( 21,210)( 22,209)( 23,208)
( 24,207)( 25,206)( 26,226)( 27,230)( 28,229)( 29,228)( 30,227)( 31,250)
( 32,249)( 33,248)( 34,247)( 35,246)( 36,245)( 37,244)( 38,243)( 39,242)
( 40,241)( 41,240)( 42,239)( 43,238)( 44,237)( 45,236)( 46,235)( 47,234)
( 48,233)( 49,232)( 50,231)( 51,251)( 52,255)( 53,254)( 54,253)( 55,252)
( 56,275)( 57,274)( 58,273)( 59,272)( 60,271)( 61,270)( 62,269)( 63,268)
( 64,267)( 65,266)( 66,265)( 67,264)( 68,263)( 69,262)( 70,261)( 71,260)
( 72,259)( 73,258)( 74,257)( 75,256)( 76,276)( 77,280)( 78,279)( 79,278)
( 80,277)( 81,300)( 82,299)( 83,298)( 84,297)( 85,296)( 86,295)( 87,294)
( 88,293)( 89,292)( 90,291)( 91,290)( 92,289)( 93,288)( 94,287)( 95,286)
( 96,285)( 97,284)( 98,283)( 99,282)(100,281)(101,301)(102,305)(103,304)
(104,303)(105,302)(106,325)(107,324)(108,323)(109,322)(110,321)(111,320)
(112,319)(113,318)(114,317)(115,316)(116,315)(117,314)(118,313)(119,312)
(120,311)(121,310)(122,309)(123,308)(124,307)(125,306)(126,326)(127,330)
(128,329)(129,328)(130,327)(131,350)(132,349)(133,348)(134,347)(135,346)
(136,345)(137,344)(138,343)(139,342)(140,341)(141,340)(142,339)(143,338)
(144,337)(145,336)(146,335)(147,334)(148,333)(149,332)(150,331)(151,351)
(152,355)(153,354)(154,353)(155,352)(156,375)(157,374)(158,373)(159,372)
(160,371)(161,370)(162,369)(163,368)(164,367)(165,366)(166,365)(167,364)
(168,363)(169,362)(170,361)(171,360)(172,359)(173,358)(174,357)(175,356)
(176,376)(177,380)(178,379)(179,378)(180,377)(181,400)(182,399)(183,398)
(184,397)(185,396)(186,395)(187,394)(188,393)(189,392)(190,391)(191,390)
(192,389)(193,388)(194,387)(195,386)(196,385)(197,384)(198,383)(199,382)
(200,381);
s2 := Sym(400)!(  1,  6)(  2, 10)(  3,  9)(  4,  8)(  5,  7)( 11, 25)( 12, 24)
( 13, 23)( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 26, 31)( 27, 35)( 28, 34)
( 29, 33)( 30, 32)( 36, 50)( 37, 49)( 38, 48)( 39, 47)( 40, 46)( 41, 45)
( 42, 44)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 75)( 62, 74)
( 63, 73)( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 76, 81)( 77, 85)( 78, 84)
( 79, 83)( 80, 82)( 86,100)( 87, 99)( 88, 98)( 89, 97)( 90, 96)( 91, 95)
( 92, 94)(101,131)(102,135)(103,134)(104,133)(105,132)(106,126)(107,130)
(108,129)(109,128)(110,127)(111,150)(112,149)(113,148)(114,147)(115,146)
(116,145)(117,144)(118,143)(119,142)(120,141)(121,140)(122,139)(123,138)
(124,137)(125,136)(151,181)(152,185)(153,184)(154,183)(155,182)(156,176)
(157,180)(158,179)(159,178)(160,177)(161,200)(162,199)(163,198)(164,197)
(165,196)(166,195)(167,194)(168,193)(169,192)(170,191)(171,190)(172,189)
(173,188)(174,187)(175,186)(201,256)(202,260)(203,259)(204,258)(205,257)
(206,251)(207,255)(208,254)(209,253)(210,252)(211,275)(212,274)(213,273)
(214,272)(215,271)(216,270)(217,269)(218,268)(219,267)(220,266)(221,265)
(222,264)(223,263)(224,262)(225,261)(226,281)(227,285)(228,284)(229,283)
(230,282)(231,276)(232,280)(233,279)(234,278)(235,277)(236,300)(237,299)
(238,298)(239,297)(240,296)(241,295)(242,294)(243,293)(244,292)(245,291)
(246,290)(247,289)(248,288)(249,287)(250,286)(301,381)(302,385)(303,384)
(304,383)(305,382)(306,376)(307,380)(308,379)(309,378)(310,377)(311,400)
(312,399)(313,398)(314,397)(315,396)(316,395)(317,394)(318,393)(319,392)
(320,391)(321,390)(322,389)(323,388)(324,387)(325,386)(326,356)(327,360)
(328,359)(329,358)(330,357)(331,351)(332,355)(333,354)(334,353)(335,352)
(336,375)(337,374)(338,373)(339,372)(340,371)(341,370)(342,369)(343,368)
(344,367)(345,366)(346,365)(347,364)(348,363)(349,362)(350,361);
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*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s0*s2*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope