Polytope of Type {8,100}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,100}*1600a
Also Known As : {8,100|2}. if this polytope has another name.
Group : SmallGroup(1600,401)
Rank : 3
Schlafli Type : {8,100}
Number of vertices, edges, etc : 8, 400, 100
Order of s₀s₁s₂ : 200
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
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, {8,50}*800
   4-fold quotients : {2,100}*400, {4,50}*400
   5-fold quotients : {8,20}*320a
   8-fold quotients : {2,50}*200
   10-fold quotients : {4,20}*160, {8,10}*160
   16-fold quotients : {2,25}*100
   20-fold quotients : {2,20}*80, {4,10}*80
   25-fold quotients : {8,4}*64a
   40-fold quotients : {2,10}*40
   50-fold quotients : {4,4}*32, {8,2}*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 := (101,126)(102,127)(103,128)(104,129)(105,130)(106,131)(107,132)(108,133)
(109,134)(110,135)(111,136)(112,137)(113,138)(114,139)(115,140)(116,141)
(117,142)(118,143)(119,144)(120,145)(121,146)(122,147)(123,148)(124,149)
(125,150)(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)(251,351)(252,352)(253,353)(254,354)
(255,355)(256,356)(257,357)(258,358)(259,359)(260,360)(261,361)(262,362)
(263,363)(264,364)(265,365)(266,366)(267,367)(268,368)(269,369)(270,370)
(271,371)(272,372)(273,373)(274,374)(275,375)(276,376)(277,377)(278,378)
(279,379)(280,380)(281,381)(282,382)(283,383)(284,384)(285,385)(286,386)
(287,387)(288,388)(289,389)(290,390)(291,391)(292,392)(293,393)(294,394)
(295,395)(296,396)(297,397)(298,398)(299,399)(300,400);;
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)(101,326)(102,330)(103,329)(104,328)
(105,327)(106,350)(107,349)(108,348)(109,347)(110,346)(111,345)(112,344)
(113,343)(114,342)(115,341)(116,340)(117,339)(118,338)(119,337)(120,336)
(121,335)(122,334)(123,333)(124,332)(125,331)(126,301)(127,305)(128,304)
(129,303)(130,302)(131,325)(132,324)(133,323)(134,322)(135,321)(136,320)
(137,319)(138,318)(139,317)(140,316)(141,315)(142,314)(143,313)(144,312)
(145,311)(146,310)(147,309)(148,308)(149,307)(150,306)(151,376)(152,380)
(153,379)(154,378)(155,377)(156,400)(157,399)(158,398)(159,397)(160,396)
(161,395)(162,394)(163,393)(164,392)(165,391)(166,390)(167,389)(168,388)
(169,387)(170,386)(171,385)(172,384)(173,383)(174,382)(175,381)(176,351)
(177,355)(178,354)(179,353)(180,352)(181,375)(182,374)(183,373)(184,372)
(185,371)(186,370)(187,369)(188,368)(189,367)(190,366)(191,365)(192,364)
(193,363)(194,362)(195,361)(196,360)(197,359)(198,358)(199,357)(200,356);;
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)
(101,106)(102,110)(103,109)(104,108)(105,107)(111,125)(112,124)(113,123)
(114,122)(115,121)(116,120)(117,119)(126,131)(127,135)(128,134)(129,133)
(130,132)(136,150)(137,149)(138,148)(139,147)(140,146)(141,145)(142,144)
(151,156)(152,160)(153,159)(154,158)(155,157)(161,175)(162,174)(163,173)
(164,172)(165,171)(166,170)(167,169)(176,181)(177,185)(178,184)(179,183)
(180,182)(186,200)(187,199)(188,198)(189,197)(190,196)(191,195)(192,194)
(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)(301,356)(302,360)(303,359)(304,358)(305,357)(306,351)
(307,355)(308,354)(309,353)(310,352)(311,375)(312,374)(313,373)(314,372)
(315,371)(316,370)(317,369)(318,368)(319,367)(320,366)(321,365)(322,364)
(323,363)(324,362)(325,361)(326,381)(327,385)(328,384)(329,383)(330,382)
(331,376)(332,380)(333,379)(334,378)(335,377)(336,400)(337,399)(338,398)
(339,397)(340,396)(341,395)(342,394)(343,393)(344,392)(345,391)(346,390)
(347,389)(348,388)(349,387)(350,386);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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)!(101,126)(102,127)(103,128)(104,129)(105,130)(106,131)(107,132)
(108,133)(109,134)(110,135)(111,136)(112,137)(113,138)(114,139)(115,140)
(116,141)(117,142)(118,143)(119,144)(120,145)(121,146)(122,147)(123,148)
(124,149)(125,150)(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)(251,351)(252,352)(253,353)
(254,354)(255,355)(256,356)(257,357)(258,358)(259,359)(260,360)(261,361)
(262,362)(263,363)(264,364)(265,365)(266,366)(267,367)(268,368)(269,369)
(270,370)(271,371)(272,372)(273,373)(274,374)(275,375)(276,376)(277,377)
(278,378)(279,379)(280,380)(281,381)(282,382)(283,383)(284,384)(285,385)
(286,386)(287,387)(288,388)(289,389)(290,390)(291,391)(292,392)(293,393)
(294,394)(295,395)(296,396)(297,397)(298,398)(299,399)(300,400);
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)(101,326)(102,330)(103,329)
(104,328)(105,327)(106,350)(107,349)(108,348)(109,347)(110,346)(111,345)
(112,344)(113,343)(114,342)(115,341)(116,340)(117,339)(118,338)(119,337)
(120,336)(121,335)(122,334)(123,333)(124,332)(125,331)(126,301)(127,305)
(128,304)(129,303)(130,302)(131,325)(132,324)(133,323)(134,322)(135,321)
(136,320)(137,319)(138,318)(139,317)(140,316)(141,315)(142,314)(143,313)
(144,312)(145,311)(146,310)(147,309)(148,308)(149,307)(150,306)(151,376)
(152,380)(153,379)(154,378)(155,377)(156,400)(157,399)(158,398)(159,397)
(160,396)(161,395)(162,394)(163,393)(164,392)(165,391)(166,390)(167,389)
(168,388)(169,387)(170,386)(171,385)(172,384)(173,383)(174,382)(175,381)
(176,351)(177,355)(178,354)(179,353)(180,352)(181,375)(182,374)(183,373)
(184,372)(185,371)(186,370)(187,369)(188,368)(189,367)(190,366)(191,365)
(192,364)(193,363)(194,362)(195,361)(196,360)(197,359)(198,358)(199,357)
(200,356);
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)(101,106)(102,110)(103,109)(104,108)(105,107)(111,125)(112,124)
(113,123)(114,122)(115,121)(116,120)(117,119)(126,131)(127,135)(128,134)
(129,133)(130,132)(136,150)(137,149)(138,148)(139,147)(140,146)(141,145)
(142,144)(151,156)(152,160)(153,159)(154,158)(155,157)(161,175)(162,174)
(163,173)(164,172)(165,171)(166,170)(167,169)(176,181)(177,185)(178,184)
(179,183)(180,182)(186,200)(187,199)(188,198)(189,197)(190,196)(191,195)
(192,194)(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)(301,356)(302,360)(303,359)(304,358)(305,357)
(306,351)(307,355)(308,354)(309,353)(310,352)(311,375)(312,374)(313,373)
(314,372)(315,371)(316,370)(317,369)(318,368)(319,367)(320,366)(321,365)
(322,364)(323,363)(324,362)(325,361)(326,381)(327,385)(328,384)(329,383)
(330,382)(331,376)(332,380)(333,379)(334,378)(335,377)(336,400)(337,399)
(338,398)(339,397)(340,396)(341,395)(342,394)(343,393)(344,392)(345,391)
(346,390)(347,389)(348,388)(349,387)(350,386);
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*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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