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# Polytope of Type {114,8}

Atlas Canonical Name : {114,8}*1824
Also Known As : {114,8|2}. if this polytope has another name.
Group : SmallGroup(1824,975)
Rank : 3
Schlafli Type : {114,8}
Number of vertices, edges, etc : 114, 456, 8
Order of s0s1s2 : 456
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 : {114,4}*912a
3-fold quotients : {38,8}*608
4-fold quotients : {114,2}*456
6-fold quotients : {38,4}*304
8-fold quotients : {57,2}*228
12-fold quotients : {38,2}*152
19-fold quotients : {6,8}*96
24-fold quotients : {19,2}*76
38-fold quotients : {6,4}*48a
57-fold quotients : {2,8}*32
76-fold quotients : {6,2}*24
114-fold quotients : {2,4}*16
152-fold quotients : {3,2}*12
228-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)(  9, 12)
( 10, 11)( 20, 39)( 21, 57)( 22, 56)( 23, 55)( 24, 54)( 25, 53)( 26, 52)
( 27, 51)( 28, 50)( 29, 49)( 30, 48)( 31, 47)( 32, 46)( 33, 45)( 34, 44)
( 35, 43)( 36, 42)( 37, 41)( 38, 40)( 59, 76)( 60, 75)( 61, 74)( 62, 73)
( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 77, 96)( 78,114)( 79,113)
( 80,112)( 81,111)( 82,110)( 83,109)( 84,108)( 85,107)( 86,106)( 87,105)
( 88,104)( 89,103)( 90,102)( 91,101)( 92,100)( 93, 99)( 94, 98)( 95, 97)
(116,133)(117,132)(118,131)(119,130)(120,129)(121,128)(122,127)(123,126)
(124,125)(134,153)(135,171)(136,170)(137,169)(138,168)(139,167)(140,166)
(141,165)(142,164)(143,163)(144,162)(145,161)(146,160)(147,159)(148,158)
(149,157)(150,156)(151,155)(152,154)(173,190)(174,189)(175,188)(176,187)
(177,186)(178,185)(179,184)(180,183)(181,182)(191,210)(192,228)(193,227)
(194,226)(195,225)(196,224)(197,223)(198,222)(199,221)(200,220)(201,219)
(202,218)(203,217)(204,216)(205,215)(206,214)(207,213)(208,212)(209,211)
(230,247)(231,246)(232,245)(233,244)(234,243)(235,242)(236,241)(237,240)
(238,239)(248,267)(249,285)(250,284)(251,283)(252,282)(253,281)(254,280)
(255,279)(256,278)(257,277)(258,276)(259,275)(260,274)(261,273)(262,272)
(263,271)(264,270)(265,269)(266,268)(287,304)(288,303)(289,302)(290,301)
(291,300)(292,299)(293,298)(294,297)(295,296)(305,324)(306,342)(307,341)
(308,340)(309,339)(310,338)(311,337)(312,336)(313,335)(314,334)(315,333)
(316,332)(317,331)(318,330)(319,329)(320,328)(321,327)(322,326)(323,325)
(344,361)(345,360)(346,359)(347,358)(348,357)(349,356)(350,355)(351,354)
(352,353)(362,381)(363,399)(364,398)(365,397)(366,396)(367,395)(368,394)
(369,393)(370,392)(371,391)(372,390)(373,389)(374,388)(375,387)(376,386)
(377,385)(378,384)(379,383)(380,382)(401,418)(402,417)(403,416)(404,415)
(405,414)(406,413)(407,412)(408,411)(409,410)(419,438)(420,456)(421,455)
(422,454)(423,453)(424,452)(425,451)(426,450)(427,449)(428,448)(429,447)
(430,446)(431,445)(432,444)(433,443)(434,442)(435,441)(436,440)(437,439);;
s1 := (  1, 21)(  2, 20)(  3, 38)(  4, 37)(  5, 36)(  6, 35)(  7, 34)(  8, 33)
(  9, 32)( 10, 31)( 11, 30)( 12, 29)( 13, 28)( 14, 27)( 15, 26)( 16, 25)
( 17, 24)( 18, 23)( 19, 22)( 39, 40)( 41, 57)( 42, 56)( 43, 55)( 44, 54)
( 45, 53)( 46, 52)( 47, 51)( 48, 50)( 58, 78)( 59, 77)( 60, 95)( 61, 94)
( 62, 93)( 63, 92)( 64, 91)( 65, 90)( 66, 89)( 67, 88)( 68, 87)( 69, 86)
( 70, 85)( 71, 84)( 72, 83)( 73, 82)( 74, 81)( 75, 80)( 76, 79)( 96, 97)
( 98,114)( 99,113)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)
(115,192)(116,191)(117,209)(118,208)(119,207)(120,206)(121,205)(122,204)
(123,203)(124,202)(125,201)(126,200)(127,199)(128,198)(129,197)(130,196)
(131,195)(132,194)(133,193)(134,173)(135,172)(136,190)(137,189)(138,188)
(139,187)(140,186)(141,185)(142,184)(143,183)(144,182)(145,181)(146,180)
(147,179)(148,178)(149,177)(150,176)(151,175)(152,174)(153,211)(154,210)
(155,228)(156,227)(157,226)(158,225)(159,224)(160,223)(161,222)(162,221)
(163,220)(164,219)(165,218)(166,217)(167,216)(168,215)(169,214)(170,213)
(171,212)(229,363)(230,362)(231,380)(232,379)(233,378)(234,377)(235,376)
(236,375)(237,374)(238,373)(239,372)(240,371)(241,370)(242,369)(243,368)
(244,367)(245,366)(246,365)(247,364)(248,344)(249,343)(250,361)(251,360)
(252,359)(253,358)(254,357)(255,356)(256,355)(257,354)(258,353)(259,352)
(260,351)(261,350)(262,349)(263,348)(264,347)(265,346)(266,345)(267,382)
(268,381)(269,399)(270,398)(271,397)(272,396)(273,395)(274,394)(275,393)
(276,392)(277,391)(278,390)(279,389)(280,388)(281,387)(282,386)(283,385)
(284,384)(285,383)(286,420)(287,419)(288,437)(289,436)(290,435)(291,434)
(292,433)(293,432)(294,431)(295,430)(296,429)(297,428)(298,427)(299,426)
(300,425)(301,424)(302,423)(303,422)(304,421)(305,401)(306,400)(307,418)
(308,417)(309,416)(310,415)(311,414)(312,413)(313,412)(314,411)(315,410)
(316,409)(317,408)(318,407)(319,406)(320,405)(321,404)(322,403)(323,402)
(324,439)(325,438)(326,456)(327,455)(328,454)(329,453)(330,452)(331,451)
(332,450)(333,449)(334,448)(335,447)(336,446)(337,445)(338,444)(339,443)
(340,442)(341,441)(342,440);;
s2 := (  1,229)(  2,230)(  3,231)(  4,232)(  5,233)(  6,234)(  7,235)(  8,236)
(  9,237)( 10,238)( 11,239)( 12,240)( 13,241)( 14,242)( 15,243)( 16,244)
( 17,245)( 18,246)( 19,247)( 20,248)( 21,249)( 22,250)( 23,251)( 24,252)
( 25,253)( 26,254)( 27,255)( 28,256)( 29,257)( 30,258)( 31,259)( 32,260)
( 33,261)( 34,262)( 35,263)( 36,264)( 37,265)( 38,266)( 39,267)( 40,268)
( 41,269)( 42,270)( 43,271)( 44,272)( 45,273)( 46,274)( 47,275)( 48,276)
( 49,277)( 50,278)( 51,279)( 52,280)( 53,281)( 54,282)( 55,283)( 56,284)
( 57,285)( 58,286)( 59,287)( 60,288)( 61,289)( 62,290)( 63,291)( 64,292)
( 65,293)( 66,294)( 67,295)( 68,296)( 69,297)( 70,298)( 71,299)( 72,300)
( 73,301)( 74,302)( 75,303)( 76,304)( 77,305)( 78,306)( 79,307)( 80,308)
( 81,309)( 82,310)( 83,311)( 84,312)( 85,313)( 86,314)( 87,315)( 88,316)
( 89,317)( 90,318)( 91,319)( 92,320)( 93,321)( 94,322)( 95,323)( 96,324)
( 97,325)( 98,326)( 99,327)(100,328)(101,329)(102,330)(103,331)(104,332)
(105,333)(106,334)(107,335)(108,336)(109,337)(110,338)(111,339)(112,340)
(113,341)(114,342)(115,400)(116,401)(117,402)(118,403)(119,404)(120,405)
(121,406)(122,407)(123,408)(124,409)(125,410)(126,411)(127,412)(128,413)
(129,414)(130,415)(131,416)(132,417)(133,418)(134,419)(135,420)(136,421)
(137,422)(138,423)(139,424)(140,425)(141,426)(142,427)(143,428)(144,429)
(145,430)(146,431)(147,432)(148,433)(149,434)(150,435)(151,436)(152,437)
(153,438)(154,439)(155,440)(156,441)(157,442)(158,443)(159,444)(160,445)
(161,446)(162,447)(163,448)(164,449)(165,450)(166,451)(167,452)(168,453)
(169,454)(170,455)(171,456)(172,343)(173,344)(174,345)(175,346)(176,347)
(177,348)(178,349)(179,350)(180,351)(181,352)(182,353)(183,354)(184,355)
(185,356)(186,357)(187,358)(188,359)(189,360)(190,361)(191,362)(192,363)
(193,364)(194,365)(195,366)(196,367)(197,368)(198,369)(199,370)(200,371)
(201,372)(202,373)(203,374)(204,375)(205,376)(206,377)(207,378)(208,379)
(209,380)(210,381)(211,382)(212,383)(213,384)(214,385)(215,386)(216,387)
(217,388)(218,389)(219,390)(220,391)(221,392)(222,393)(223,394)(224,395)
(225,396)(226,397)(227,398)(228,399);;
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,
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*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(456)!(  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)
(  9, 12)( 10, 11)( 20, 39)( 21, 57)( 22, 56)( 23, 55)( 24, 54)( 25, 53)
( 26, 52)( 27, 51)( 28, 50)( 29, 49)( 30, 48)( 31, 47)( 32, 46)( 33, 45)
( 34, 44)( 35, 43)( 36, 42)( 37, 41)( 38, 40)( 59, 76)( 60, 75)( 61, 74)
( 62, 73)( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 77, 96)( 78,114)
( 79,113)( 80,112)( 81,111)( 82,110)( 83,109)( 84,108)( 85,107)( 86,106)
( 87,105)( 88,104)( 89,103)( 90,102)( 91,101)( 92,100)( 93, 99)( 94, 98)
( 95, 97)(116,133)(117,132)(118,131)(119,130)(120,129)(121,128)(122,127)
(123,126)(124,125)(134,153)(135,171)(136,170)(137,169)(138,168)(139,167)
(140,166)(141,165)(142,164)(143,163)(144,162)(145,161)(146,160)(147,159)
(148,158)(149,157)(150,156)(151,155)(152,154)(173,190)(174,189)(175,188)
(176,187)(177,186)(178,185)(179,184)(180,183)(181,182)(191,210)(192,228)
(193,227)(194,226)(195,225)(196,224)(197,223)(198,222)(199,221)(200,220)
(201,219)(202,218)(203,217)(204,216)(205,215)(206,214)(207,213)(208,212)
(209,211)(230,247)(231,246)(232,245)(233,244)(234,243)(235,242)(236,241)
(237,240)(238,239)(248,267)(249,285)(250,284)(251,283)(252,282)(253,281)
(254,280)(255,279)(256,278)(257,277)(258,276)(259,275)(260,274)(261,273)
(262,272)(263,271)(264,270)(265,269)(266,268)(287,304)(288,303)(289,302)
(290,301)(291,300)(292,299)(293,298)(294,297)(295,296)(305,324)(306,342)
(307,341)(308,340)(309,339)(310,338)(311,337)(312,336)(313,335)(314,334)
(315,333)(316,332)(317,331)(318,330)(319,329)(320,328)(321,327)(322,326)
(323,325)(344,361)(345,360)(346,359)(347,358)(348,357)(349,356)(350,355)
(351,354)(352,353)(362,381)(363,399)(364,398)(365,397)(366,396)(367,395)
(368,394)(369,393)(370,392)(371,391)(372,390)(373,389)(374,388)(375,387)
(376,386)(377,385)(378,384)(379,383)(380,382)(401,418)(402,417)(403,416)
(404,415)(405,414)(406,413)(407,412)(408,411)(409,410)(419,438)(420,456)
(421,455)(422,454)(423,453)(424,452)(425,451)(426,450)(427,449)(428,448)
(429,447)(430,446)(431,445)(432,444)(433,443)(434,442)(435,441)(436,440)
(437,439);
s1 := Sym(456)!(  1, 21)(  2, 20)(  3, 38)(  4, 37)(  5, 36)(  6, 35)(  7, 34)
(  8, 33)(  9, 32)( 10, 31)( 11, 30)( 12, 29)( 13, 28)( 14, 27)( 15, 26)
( 16, 25)( 17, 24)( 18, 23)( 19, 22)( 39, 40)( 41, 57)( 42, 56)( 43, 55)
( 44, 54)( 45, 53)( 46, 52)( 47, 51)( 48, 50)( 58, 78)( 59, 77)( 60, 95)
( 61, 94)( 62, 93)( 63, 92)( 64, 91)( 65, 90)( 66, 89)( 67, 88)( 68, 87)
( 69, 86)( 70, 85)( 71, 84)( 72, 83)( 73, 82)( 74, 81)( 75, 80)( 76, 79)
( 96, 97)( 98,114)( 99,113)(100,112)(101,111)(102,110)(103,109)(104,108)
(105,107)(115,192)(116,191)(117,209)(118,208)(119,207)(120,206)(121,205)
(122,204)(123,203)(124,202)(125,201)(126,200)(127,199)(128,198)(129,197)
(130,196)(131,195)(132,194)(133,193)(134,173)(135,172)(136,190)(137,189)
(138,188)(139,187)(140,186)(141,185)(142,184)(143,183)(144,182)(145,181)
(146,180)(147,179)(148,178)(149,177)(150,176)(151,175)(152,174)(153,211)
(154,210)(155,228)(156,227)(157,226)(158,225)(159,224)(160,223)(161,222)
(162,221)(163,220)(164,219)(165,218)(166,217)(167,216)(168,215)(169,214)
(170,213)(171,212)(229,363)(230,362)(231,380)(232,379)(233,378)(234,377)
(235,376)(236,375)(237,374)(238,373)(239,372)(240,371)(241,370)(242,369)
(243,368)(244,367)(245,366)(246,365)(247,364)(248,344)(249,343)(250,361)
(251,360)(252,359)(253,358)(254,357)(255,356)(256,355)(257,354)(258,353)
(259,352)(260,351)(261,350)(262,349)(263,348)(264,347)(265,346)(266,345)
(267,382)(268,381)(269,399)(270,398)(271,397)(272,396)(273,395)(274,394)
(275,393)(276,392)(277,391)(278,390)(279,389)(280,388)(281,387)(282,386)
(283,385)(284,384)(285,383)(286,420)(287,419)(288,437)(289,436)(290,435)
(291,434)(292,433)(293,432)(294,431)(295,430)(296,429)(297,428)(298,427)
(299,426)(300,425)(301,424)(302,423)(303,422)(304,421)(305,401)(306,400)
(307,418)(308,417)(309,416)(310,415)(311,414)(312,413)(313,412)(314,411)
(315,410)(316,409)(317,408)(318,407)(319,406)(320,405)(321,404)(322,403)
(323,402)(324,439)(325,438)(326,456)(327,455)(328,454)(329,453)(330,452)
(331,451)(332,450)(333,449)(334,448)(335,447)(336,446)(337,445)(338,444)
(339,443)(340,442)(341,441)(342,440);
s2 := Sym(456)!(  1,229)(  2,230)(  3,231)(  4,232)(  5,233)(  6,234)(  7,235)
(  8,236)(  9,237)( 10,238)( 11,239)( 12,240)( 13,241)( 14,242)( 15,243)
( 16,244)( 17,245)( 18,246)( 19,247)( 20,248)( 21,249)( 22,250)( 23,251)
( 24,252)( 25,253)( 26,254)( 27,255)( 28,256)( 29,257)( 30,258)( 31,259)
( 32,260)( 33,261)( 34,262)( 35,263)( 36,264)( 37,265)( 38,266)( 39,267)
( 40,268)( 41,269)( 42,270)( 43,271)( 44,272)( 45,273)( 46,274)( 47,275)
( 48,276)( 49,277)( 50,278)( 51,279)( 52,280)( 53,281)( 54,282)( 55,283)
( 56,284)( 57,285)( 58,286)( 59,287)( 60,288)( 61,289)( 62,290)( 63,291)
( 64,292)( 65,293)( 66,294)( 67,295)( 68,296)( 69,297)( 70,298)( 71,299)
( 72,300)( 73,301)( 74,302)( 75,303)( 76,304)( 77,305)( 78,306)( 79,307)
( 80,308)( 81,309)( 82,310)( 83,311)( 84,312)( 85,313)( 86,314)( 87,315)
( 88,316)( 89,317)( 90,318)( 91,319)( 92,320)( 93,321)( 94,322)( 95,323)
( 96,324)( 97,325)( 98,326)( 99,327)(100,328)(101,329)(102,330)(103,331)
(104,332)(105,333)(106,334)(107,335)(108,336)(109,337)(110,338)(111,339)
(112,340)(113,341)(114,342)(115,400)(116,401)(117,402)(118,403)(119,404)
(120,405)(121,406)(122,407)(123,408)(124,409)(125,410)(126,411)(127,412)
(128,413)(129,414)(130,415)(131,416)(132,417)(133,418)(134,419)(135,420)
(136,421)(137,422)(138,423)(139,424)(140,425)(141,426)(142,427)(143,428)
(144,429)(145,430)(146,431)(147,432)(148,433)(149,434)(150,435)(151,436)
(152,437)(153,438)(154,439)(155,440)(156,441)(157,442)(158,443)(159,444)
(160,445)(161,446)(162,447)(163,448)(164,449)(165,450)(166,451)(167,452)
(168,453)(169,454)(170,455)(171,456)(172,343)(173,344)(174,345)(175,346)
(176,347)(177,348)(178,349)(179,350)(180,351)(181,352)(182,353)(183,354)
(184,355)(185,356)(186,357)(187,358)(188,359)(189,360)(190,361)(191,362)
(192,363)(193,364)(194,365)(195,366)(196,367)(197,368)(198,369)(199,370)
(200,371)(201,372)(202,373)(203,374)(204,375)(205,376)(206,377)(207,378)
(208,379)(209,380)(210,381)(211,382)(212,383)(213,384)(214,385)(215,386)
(216,387)(217,388)(218,389)(219,390)(220,391)(221,392)(222,393)(223,394)
(224,395)(225,396)(226,397)(227,398)(228,399);
poly := sub<Sym(456)|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,
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*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