Polytope of Type {100,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {100,4}*1600
if this polytope has a name.
Group : SmallGroup(1600,368)
Rank : 3
Schlafli Type : {100,4}
Number of vertices, edges, etc : 200, 400, 8
Order of s₀s₁s₂ : 100
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {100,4}*800
   4-fold quotients : {100,2}*400, {50,4}*400
   5-fold quotients : {20,4}*320
   8-fold quotients : {50,2}*200
   10-fold quotients : {20,4}*160
   16-fold quotients : {25,2}*100
   20-fold quotients : {20,2}*80, {10,4}*80
   25-fold quotients : {4,4}*64
   40-fold quotients : {10,2}*40
   50-fold quotients : {4,4}*32
   80-fold quotients : {5,2}*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 := (  2,  5)(  3,  4)(  6, 25)(  7, 24)(  8, 23)(  9, 22)( 10, 21)( 11, 20)
( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 27, 30)( 28, 29)( 31, 50)( 32, 49)
( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)( 38, 43)( 39, 42)( 40, 41)
( 52, 55)( 53, 54)( 56, 75)( 57, 74)( 58, 73)( 59, 72)( 60, 71)( 61, 70)
( 62, 69)( 63, 68)( 64, 67)( 65, 66)( 77, 80)( 78, 79)( 81,100)( 82, 99)
( 83, 98)( 84, 97)( 85, 96)( 86, 95)( 87, 94)( 88, 93)( 89, 92)( 90, 91)
(101,126)(102,130)(103,129)(104,128)(105,127)(106,150)(107,149)(108,148)
(109,147)(110,146)(111,145)(112,144)(113,143)(114,142)(115,141)(116,140)
(117,139)(118,138)(119,137)(120,136)(121,135)(122,134)(123,133)(124,132)
(125,131)(151,176)(152,180)(153,179)(154,178)(155,177)(156,200)(157,199)
(158,198)(159,197)(160,196)(161,195)(162,194)(163,193)(164,192)(165,191)
(166,190)(167,189)(168,188)(169,187)(170,186)(171,185)(172,184)(173,183)
(174,182)(175,181)(201,251)(202,255)(203,254)(204,253)(205,252)(206,275)
(207,274)(208,273)(209,272)(210,271)(211,270)(212,269)(213,268)(214,267)
(215,266)(216,265)(217,264)(218,263)(219,262)(220,261)(221,260)(222,259)
(223,258)(224,257)(225,256)(226,276)(227,280)(228,279)(229,278)(230,277)
(231,300)(232,299)(233,298)(234,297)(235,296)(236,295)(237,294)(238,293)
(239,292)(240,291)(241,290)(242,289)(243,288)(244,287)(245,286)(246,285)
(247,284)(248,283)(249,282)(250,281)(301,376)(302,380)(303,379)(304,378)
(305,377)(306,400)(307,399)(308,398)(309,397)(310,396)(311,395)(312,394)
(313,393)(314,392)(315,391)(316,390)(317,389)(318,388)(319,387)(320,386)
(321,385)(322,384)(323,383)(324,382)(325,381)(326,351)(327,355)(328,354)
(329,353)(330,352)(331,375)(332,374)(333,373)(334,372)(335,371)(336,370)
(337,369)(338,368)(339,367)(340,366)(341,365)(342,364)(343,363)(344,362)
(345,361)(346,360)(347,359)(348,358)(349,357)(350,356);;
s1 := (  1,206)(  2,210)(  3,209)(  4,208)(  5,207)(  6,201)(  7,205)(  8,204)
(  9,203)( 10,202)( 11,225)( 12,224)( 13,223)( 14,222)( 15,221)( 16,220)
( 17,219)( 18,218)( 19,217)( 20,216)( 21,215)( 22,214)( 23,213)( 24,212)
( 25,211)( 26,231)( 27,235)( 28,234)( 29,233)( 30,232)( 31,226)( 32,230)
( 33,229)( 34,228)( 35,227)( 36,250)( 37,249)( 38,248)( 39,247)( 40,246)
( 41,245)( 42,244)( 43,243)( 44,242)( 45,241)( 46,240)( 47,239)( 48,238)
( 49,237)( 50,236)( 51,256)( 52,260)( 53,259)( 54,258)( 55,257)( 56,251)
( 57,255)( 58,254)( 59,253)( 60,252)( 61,275)( 62,274)( 63,273)( 64,272)
( 65,271)( 66,270)( 67,269)( 68,268)( 69,267)( 70,266)( 71,265)( 72,264)
( 73,263)( 74,262)( 75,261)( 76,281)( 77,285)( 78,284)( 79,283)( 80,282)
( 81,276)( 82,280)( 83,279)( 84,278)( 85,277)( 86,300)( 87,299)( 88,298)
( 89,297)( 90,296)( 91,295)( 92,294)( 93,293)( 94,292)( 95,291)( 96,290)
( 97,289)( 98,288)( 99,287)(100,286)(101,306)(102,310)(103,309)(104,308)
(105,307)(106,301)(107,305)(108,304)(109,303)(110,302)(111,325)(112,324)
(113,323)(114,322)(115,321)(116,320)(117,319)(118,318)(119,317)(120,316)
(121,315)(122,314)(123,313)(124,312)(125,311)(126,331)(127,335)(128,334)
(129,333)(130,332)(131,326)(132,330)(133,329)(134,328)(135,327)(136,350)
(137,349)(138,348)(139,347)(140,346)(141,345)(142,344)(143,343)(144,342)
(145,341)(146,340)(147,339)(148,338)(149,337)(150,336)(151,356)(152,360)
(153,359)(154,358)(155,357)(156,351)(157,355)(158,354)(159,353)(160,352)
(161,375)(162,374)(163,373)(164,372)(165,371)(166,370)(167,369)(168,368)
(169,367)(170,366)(171,365)(172,364)(173,363)(174,362)(175,361)(176,381)
(177,385)(178,384)(179,383)(180,382)(181,376)(182,380)(183,379)(184,378)
(185,377)(186,400)(187,399)(188,398)(189,397)(190,396)(191,395)(192,394)
(193,393)(194,392)(195,391)(196,390)(197,389)(198,388)(199,387)(200,386);;
s2 := ( 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);;
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(400)!(  2,  5)(  3,  4)(  6, 25)(  7, 24)(  8, 23)(  9, 22)( 10, 21)
( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 27, 30)( 28, 29)( 31, 50)
( 32, 49)( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)( 38, 43)( 39, 42)
( 40, 41)( 52, 55)( 53, 54)( 56, 75)( 57, 74)( 58, 73)( 59, 72)( 60, 71)
( 61, 70)( 62, 69)( 63, 68)( 64, 67)( 65, 66)( 77, 80)( 78, 79)( 81,100)
( 82, 99)( 83, 98)( 84, 97)( 85, 96)( 86, 95)( 87, 94)( 88, 93)( 89, 92)
( 90, 91)(101,126)(102,130)(103,129)(104,128)(105,127)(106,150)(107,149)
(108,148)(109,147)(110,146)(111,145)(112,144)(113,143)(114,142)(115,141)
(116,140)(117,139)(118,138)(119,137)(120,136)(121,135)(122,134)(123,133)
(124,132)(125,131)(151,176)(152,180)(153,179)(154,178)(155,177)(156,200)
(157,199)(158,198)(159,197)(160,196)(161,195)(162,194)(163,193)(164,192)
(165,191)(166,190)(167,189)(168,188)(169,187)(170,186)(171,185)(172,184)
(173,183)(174,182)(175,181)(201,251)(202,255)(203,254)(204,253)(205,252)
(206,275)(207,274)(208,273)(209,272)(210,271)(211,270)(212,269)(213,268)
(214,267)(215,266)(216,265)(217,264)(218,263)(219,262)(220,261)(221,260)
(222,259)(223,258)(224,257)(225,256)(226,276)(227,280)(228,279)(229,278)
(230,277)(231,300)(232,299)(233,298)(234,297)(235,296)(236,295)(237,294)
(238,293)(239,292)(240,291)(241,290)(242,289)(243,288)(244,287)(245,286)
(246,285)(247,284)(248,283)(249,282)(250,281)(301,376)(302,380)(303,379)
(304,378)(305,377)(306,400)(307,399)(308,398)(309,397)(310,396)(311,395)
(312,394)(313,393)(314,392)(315,391)(316,390)(317,389)(318,388)(319,387)
(320,386)(321,385)(322,384)(323,383)(324,382)(325,381)(326,351)(327,355)
(328,354)(329,353)(330,352)(331,375)(332,374)(333,373)(334,372)(335,371)
(336,370)(337,369)(338,368)(339,367)(340,366)(341,365)(342,364)(343,363)
(344,362)(345,361)(346,360)(347,359)(348,358)(349,357)(350,356);
s1 := Sym(400)!(  1,206)(  2,210)(  3,209)(  4,208)(  5,207)(  6,201)(  7,205)
(  8,204)(  9,203)( 10,202)( 11,225)( 12,224)( 13,223)( 14,222)( 15,221)
( 16,220)( 17,219)( 18,218)( 19,217)( 20,216)( 21,215)( 22,214)( 23,213)
( 24,212)( 25,211)( 26,231)( 27,235)( 28,234)( 29,233)( 30,232)( 31,226)
( 32,230)( 33,229)( 34,228)( 35,227)( 36,250)( 37,249)( 38,248)( 39,247)
( 40,246)( 41,245)( 42,244)( 43,243)( 44,242)( 45,241)( 46,240)( 47,239)
( 48,238)( 49,237)( 50,236)( 51,256)( 52,260)( 53,259)( 54,258)( 55,257)
( 56,251)( 57,255)( 58,254)( 59,253)( 60,252)( 61,275)( 62,274)( 63,273)
( 64,272)( 65,271)( 66,270)( 67,269)( 68,268)( 69,267)( 70,266)( 71,265)
( 72,264)( 73,263)( 74,262)( 75,261)( 76,281)( 77,285)( 78,284)( 79,283)
( 80,282)( 81,276)( 82,280)( 83,279)( 84,278)( 85,277)( 86,300)( 87,299)
( 88,298)( 89,297)( 90,296)( 91,295)( 92,294)( 93,293)( 94,292)( 95,291)
( 96,290)( 97,289)( 98,288)( 99,287)(100,286)(101,306)(102,310)(103,309)
(104,308)(105,307)(106,301)(107,305)(108,304)(109,303)(110,302)(111,325)
(112,324)(113,323)(114,322)(115,321)(116,320)(117,319)(118,318)(119,317)
(120,316)(121,315)(122,314)(123,313)(124,312)(125,311)(126,331)(127,335)
(128,334)(129,333)(130,332)(131,326)(132,330)(133,329)(134,328)(135,327)
(136,350)(137,349)(138,348)(139,347)(140,346)(141,345)(142,344)(143,343)
(144,342)(145,341)(146,340)(147,339)(148,338)(149,337)(150,336)(151,356)
(152,360)(153,359)(154,358)(155,357)(156,351)(157,355)(158,354)(159,353)
(160,352)(161,375)(162,374)(163,373)(164,372)(165,371)(166,370)(167,369)
(168,368)(169,367)(170,366)(171,365)(172,364)(173,363)(174,362)(175,361)
(176,381)(177,385)(178,384)(179,383)(180,382)(181,376)(182,380)(183,379)
(184,378)(185,377)(186,400)(187,399)(188,398)(189,397)(190,396)(191,395)
(192,394)(193,393)(194,392)(195,391)(196,390)(197,389)(198,388)(199,387)
(200,386);
s2 := 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);
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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