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Polytope of Type {4,4,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,6,4}*768a
Also Known As : {{4,4|2},{4,6|2},{6,4|2}}. if this polytope has another name.
Group : SmallGroup(768,364857)
Rank : 5
Schlafli Type : {4,4,6,4}
Number of vertices, edges, etc : 4, 8, 12, 12, 4
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Universal
   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 : {4,4,6,2}*384, {2,4,6,4}*384a, {4,2,6,4}*384a
   3-fold quotients : {4,4,2,4}*256
   4-fold quotients : {2,2,6,4}*192a, {2,4,6,2}*192a, {4,2,6,2}*192
   6-fold quotients : {4,4,2,2}*128, {2,4,2,4}*128, {4,2,2,4}*128
   8-fold quotients : {4,2,3,2}*96, {2,2,6,2}*96
   12-fold quotients : {2,2,2,4}*64, {2,4,2,2}*64, {4,2,2,2}*64
   16-fold quotients : {2,2,3,2}*48
   24-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,241)(  2,242)(  3,243)(  4,244)(  5,245)(  6,246)(  7,247)(  8,248)
(  9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)( 16,256)
( 17,257)( 18,258)( 19,259)( 20,260)( 21,261)( 22,262)( 23,263)( 24,264)
( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)( 32,272)
( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)( 40,280)
( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)( 48,288)
( 49,193)( 50,194)( 51,195)( 52,196)( 53,197)( 54,198)( 55,199)( 56,200)
( 57,201)( 58,202)( 59,203)( 60,204)( 61,205)( 62,206)( 63,207)( 64,208)
( 65,209)( 66,210)( 67,211)( 68,212)( 69,213)( 70,214)( 71,215)( 72,216)
( 73,217)( 74,218)( 75,219)( 76,220)( 77,221)( 78,222)( 79,223)( 80,224)
( 81,225)( 82,226)( 83,227)( 84,228)( 85,229)( 86,230)( 87,231)( 88,232)
( 89,233)( 90,234)( 91,235)( 92,236)( 93,237)( 94,238)( 95,239)( 96,240)
( 97,340)( 98,341)( 99,342)(100,337)(101,338)(102,339)(103,346)(104,347)
(105,348)(106,343)(107,344)(108,345)(109,352)(110,353)(111,354)(112,349)
(113,350)(114,351)(115,358)(116,359)(117,360)(118,355)(119,356)(120,357)
(121,364)(122,365)(123,366)(124,361)(125,362)(126,363)(127,370)(128,371)
(129,372)(130,367)(131,368)(132,369)(133,376)(134,377)(135,378)(136,373)
(137,374)(138,375)(139,382)(140,383)(141,384)(142,379)(143,380)(144,381)
(145,292)(146,293)(147,294)(148,289)(149,290)(150,291)(151,298)(152,299)
(153,300)(154,295)(155,296)(156,297)(157,304)(158,305)(159,306)(160,301)
(161,302)(162,303)(163,310)(164,311)(165,312)(166,307)(167,308)(168,309)
(169,316)(170,317)(171,318)(172,313)(173,314)(174,315)(175,322)(176,323)
(177,324)(178,319)(179,320)(180,321)(181,328)(182,329)(183,330)(184,325)
(185,326)(186,327)(187,334)(188,335)(189,336)(190,331)(191,332)(192,333);;
s1 := ( 97,103)( 98,104)( 99,105)(100,106)(101,107)(102,108)(109,115)(110,116)
(111,117)(112,118)(113,119)(114,120)(121,127)(122,128)(123,129)(124,130)
(125,131)(126,132)(133,139)(134,140)(135,141)(136,142)(137,143)(138,144)
(145,151)(146,152)(147,153)(148,154)(149,155)(150,156)(157,163)(158,164)
(159,165)(160,166)(161,167)(162,168)(169,175)(170,176)(171,177)(172,178)
(173,179)(174,180)(181,187)(182,188)(183,189)(184,190)(185,191)(186,192)
(193,205)(194,206)(195,207)(196,208)(197,209)(198,210)(199,211)(200,212)
(201,213)(202,214)(203,215)(204,216)(217,229)(218,230)(219,231)(220,232)
(221,233)(222,234)(223,235)(224,236)(225,237)(226,238)(227,239)(228,240)
(241,253)(242,254)(243,255)(244,256)(245,257)(246,258)(247,259)(248,260)
(249,261)(250,262)(251,263)(252,264)(265,277)(266,278)(267,279)(268,280)
(269,281)(270,282)(271,283)(272,284)(273,285)(274,286)(275,287)(276,288)
(289,307)(290,308)(291,309)(292,310)(293,311)(294,312)(295,301)(296,302)
(297,303)(298,304)(299,305)(300,306)(313,331)(314,332)(315,333)(316,334)
(317,335)(318,336)(319,325)(320,326)(321,327)(322,328)(323,329)(324,330)
(337,355)(338,356)(339,357)(340,358)(341,359)(342,360)(343,349)(344,350)
(345,351)(346,352)(347,353)(348,354)(361,379)(362,380)(363,381)(364,382)
(365,383)(366,384)(367,373)(368,374)(369,375)(370,376)(371,377)(372,378);;
s2 := (  1,121)(  2,123)(  3,122)(  4,124)(  5,126)(  6,125)(  7,127)(  8,129)
(  9,128)( 10,130)( 11,132)( 12,131)( 13,133)( 14,135)( 15,134)( 16,136)
( 17,138)( 18,137)( 19,139)( 20,141)( 21,140)( 22,142)( 23,144)( 24,143)
( 25, 97)( 26, 99)( 27, 98)( 28,100)( 29,102)( 30,101)( 31,103)( 32,105)
( 33,104)( 34,106)( 35,108)( 36,107)( 37,109)( 38,111)( 39,110)( 40,112)
( 41,114)( 42,113)( 43,115)( 44,117)( 45,116)( 46,118)( 47,120)( 48,119)
( 49,172)( 50,174)( 51,173)( 52,169)( 53,171)( 54,170)( 55,178)( 56,180)
( 57,179)( 58,175)( 59,177)( 60,176)( 61,184)( 62,186)( 63,185)( 64,181)
( 65,183)( 66,182)( 67,190)( 68,192)( 69,191)( 70,187)( 71,189)( 72,188)
( 73,148)( 74,150)( 75,149)( 76,145)( 77,147)( 78,146)( 79,154)( 80,156)
( 81,155)( 82,151)( 83,153)( 84,152)( 85,160)( 86,162)( 87,161)( 88,157)
( 89,159)( 90,158)( 91,166)( 92,168)( 93,167)( 94,163)( 95,165)( 96,164)
(193,313)(194,315)(195,314)(196,316)(197,318)(198,317)(199,319)(200,321)
(201,320)(202,322)(203,324)(204,323)(205,325)(206,327)(207,326)(208,328)
(209,330)(210,329)(211,331)(212,333)(213,332)(214,334)(215,336)(216,335)
(217,289)(218,291)(219,290)(220,292)(221,294)(222,293)(223,295)(224,297)
(225,296)(226,298)(227,300)(228,299)(229,301)(230,303)(231,302)(232,304)
(233,306)(234,305)(235,307)(236,309)(237,308)(238,310)(239,312)(240,311)
(241,364)(242,366)(243,365)(244,361)(245,363)(246,362)(247,370)(248,372)
(249,371)(250,367)(251,369)(252,368)(253,376)(254,378)(255,377)(256,373)
(257,375)(258,374)(259,382)(260,384)(261,383)(262,379)(263,381)(264,380)
(265,340)(266,342)(267,341)(268,337)(269,339)(270,338)(271,346)(272,348)
(273,347)(274,343)(275,345)(276,344)(277,352)(278,354)(279,353)(280,349)
(281,351)(282,350)(283,358)(284,360)(285,359)(286,355)(287,357)(288,356);;
s3 := (  1, 27)(  2, 26)(  3, 25)(  4, 30)(  5, 29)(  6, 28)(  7, 33)(  8, 32)
(  9, 31)( 10, 36)( 11, 35)( 12, 34)( 13, 39)( 14, 38)( 15, 37)( 16, 42)
( 17, 41)( 18, 40)( 19, 45)( 20, 44)( 21, 43)( 22, 48)( 23, 47)( 24, 46)
( 49, 75)( 50, 74)( 51, 73)( 52, 78)( 53, 77)( 54, 76)( 55, 81)( 56, 80)
( 57, 79)( 58, 84)( 59, 83)( 60, 82)( 61, 87)( 62, 86)( 63, 85)( 64, 90)
( 65, 89)( 66, 88)( 67, 93)( 68, 92)( 69, 91)( 70, 96)( 71, 95)( 72, 94)
( 97,123)( 98,122)( 99,121)(100,126)(101,125)(102,124)(103,129)(104,128)
(105,127)(106,132)(107,131)(108,130)(109,135)(110,134)(111,133)(112,138)
(113,137)(114,136)(115,141)(116,140)(117,139)(118,144)(119,143)(120,142)
(145,171)(146,170)(147,169)(148,174)(149,173)(150,172)(151,177)(152,176)
(153,175)(154,180)(155,179)(156,178)(157,183)(158,182)(159,181)(160,186)
(161,185)(162,184)(163,189)(164,188)(165,187)(166,192)(167,191)(168,190)
(193,219)(194,218)(195,217)(196,222)(197,221)(198,220)(199,225)(200,224)
(201,223)(202,228)(203,227)(204,226)(205,231)(206,230)(207,229)(208,234)
(209,233)(210,232)(211,237)(212,236)(213,235)(214,240)(215,239)(216,238)
(241,267)(242,266)(243,265)(244,270)(245,269)(246,268)(247,273)(248,272)
(249,271)(250,276)(251,275)(252,274)(253,279)(254,278)(255,277)(256,282)
(257,281)(258,280)(259,285)(260,284)(261,283)(262,288)(263,287)(264,286)
(289,315)(290,314)(291,313)(292,318)(293,317)(294,316)(295,321)(296,320)
(297,319)(298,324)(299,323)(300,322)(301,327)(302,326)(303,325)(304,330)
(305,329)(306,328)(307,333)(308,332)(309,331)(310,336)(311,335)(312,334)
(337,363)(338,362)(339,361)(340,366)(341,365)(342,364)(343,369)(344,368)
(345,367)(346,372)(347,371)(348,370)(349,375)(350,374)(351,373)(352,378)
(353,377)(354,376)(355,381)(356,380)(357,379)(358,384)(359,383)(360,382);;
s4 := (  1, 49)(  2, 50)(  3, 51)(  4, 52)(  5, 53)(  6, 54)(  7, 55)(  8, 56)
(  9, 57)( 10, 58)( 11, 59)( 12, 60)( 13, 61)( 14, 62)( 15, 63)( 16, 64)
( 17, 65)( 18, 66)( 19, 67)( 20, 68)( 21, 69)( 22, 70)( 23, 71)( 24, 72)
( 25, 76)( 26, 77)( 27, 78)( 28, 73)( 29, 74)( 30, 75)( 31, 82)( 32, 83)
( 33, 84)( 34, 79)( 35, 80)( 36, 81)( 37, 88)( 38, 89)( 39, 90)( 40, 85)
( 41, 86)( 42, 87)( 43, 94)( 44, 95)( 45, 96)( 46, 91)( 47, 92)( 48, 93)
( 97,145)( 98,146)( 99,147)(100,148)(101,149)(102,150)(103,151)(104,152)
(105,153)(106,154)(107,155)(108,156)(109,157)(110,158)(111,159)(112,160)
(113,161)(114,162)(115,163)(116,164)(117,165)(118,166)(119,167)(120,168)
(121,172)(122,173)(123,174)(124,169)(125,170)(126,171)(127,178)(128,179)
(129,180)(130,175)(131,176)(132,177)(133,184)(134,185)(135,186)(136,181)
(137,182)(138,183)(139,190)(140,191)(141,192)(142,187)(143,188)(144,189)
(193,241)(194,242)(195,243)(196,244)(197,245)(198,246)(199,247)(200,248)
(201,249)(202,250)(203,251)(204,252)(205,253)(206,254)(207,255)(208,256)
(209,257)(210,258)(211,259)(212,260)(213,261)(214,262)(215,263)(216,264)
(217,268)(218,269)(219,270)(220,265)(221,266)(222,267)(223,274)(224,275)
(225,276)(226,271)(227,272)(228,273)(229,280)(230,281)(231,282)(232,277)
(233,278)(234,279)(235,286)(236,287)(237,288)(238,283)(239,284)(240,285)
(289,337)(290,338)(291,339)(292,340)(293,341)(294,342)(295,343)(296,344)
(297,345)(298,346)(299,347)(300,348)(301,349)(302,350)(303,351)(304,352)
(305,353)(306,354)(307,355)(308,356)(309,357)(310,358)(311,359)(312,360)
(313,364)(314,365)(315,366)(316,361)(317,362)(318,363)(319,370)(320,371)
(321,372)(322,367)(323,368)(324,369)(325,376)(326,377)(327,378)(328,373)
(329,374)(330,375)(331,382)(332,383)(333,384)(334,379)(335,380)(336,381);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(384)!(  1,241)(  2,242)(  3,243)(  4,244)(  5,245)(  6,246)(  7,247)
(  8,248)(  9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)
( 16,256)( 17,257)( 18,258)( 19,259)( 20,260)( 21,261)( 22,262)( 23,263)
( 24,264)( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)
( 32,272)( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)
( 40,280)( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)
( 48,288)( 49,193)( 50,194)( 51,195)( 52,196)( 53,197)( 54,198)( 55,199)
( 56,200)( 57,201)( 58,202)( 59,203)( 60,204)( 61,205)( 62,206)( 63,207)
( 64,208)( 65,209)( 66,210)( 67,211)( 68,212)( 69,213)( 70,214)( 71,215)
( 72,216)( 73,217)( 74,218)( 75,219)( 76,220)( 77,221)( 78,222)( 79,223)
( 80,224)( 81,225)( 82,226)( 83,227)( 84,228)( 85,229)( 86,230)( 87,231)
( 88,232)( 89,233)( 90,234)( 91,235)( 92,236)( 93,237)( 94,238)( 95,239)
( 96,240)( 97,340)( 98,341)( 99,342)(100,337)(101,338)(102,339)(103,346)
(104,347)(105,348)(106,343)(107,344)(108,345)(109,352)(110,353)(111,354)
(112,349)(113,350)(114,351)(115,358)(116,359)(117,360)(118,355)(119,356)
(120,357)(121,364)(122,365)(123,366)(124,361)(125,362)(126,363)(127,370)
(128,371)(129,372)(130,367)(131,368)(132,369)(133,376)(134,377)(135,378)
(136,373)(137,374)(138,375)(139,382)(140,383)(141,384)(142,379)(143,380)
(144,381)(145,292)(146,293)(147,294)(148,289)(149,290)(150,291)(151,298)
(152,299)(153,300)(154,295)(155,296)(156,297)(157,304)(158,305)(159,306)
(160,301)(161,302)(162,303)(163,310)(164,311)(165,312)(166,307)(167,308)
(168,309)(169,316)(170,317)(171,318)(172,313)(173,314)(174,315)(175,322)
(176,323)(177,324)(178,319)(179,320)(180,321)(181,328)(182,329)(183,330)
(184,325)(185,326)(186,327)(187,334)(188,335)(189,336)(190,331)(191,332)
(192,333);
s1 := Sym(384)!( 97,103)( 98,104)( 99,105)(100,106)(101,107)(102,108)(109,115)
(110,116)(111,117)(112,118)(113,119)(114,120)(121,127)(122,128)(123,129)
(124,130)(125,131)(126,132)(133,139)(134,140)(135,141)(136,142)(137,143)
(138,144)(145,151)(146,152)(147,153)(148,154)(149,155)(150,156)(157,163)
(158,164)(159,165)(160,166)(161,167)(162,168)(169,175)(170,176)(171,177)
(172,178)(173,179)(174,180)(181,187)(182,188)(183,189)(184,190)(185,191)
(186,192)(193,205)(194,206)(195,207)(196,208)(197,209)(198,210)(199,211)
(200,212)(201,213)(202,214)(203,215)(204,216)(217,229)(218,230)(219,231)
(220,232)(221,233)(222,234)(223,235)(224,236)(225,237)(226,238)(227,239)
(228,240)(241,253)(242,254)(243,255)(244,256)(245,257)(246,258)(247,259)
(248,260)(249,261)(250,262)(251,263)(252,264)(265,277)(266,278)(267,279)
(268,280)(269,281)(270,282)(271,283)(272,284)(273,285)(274,286)(275,287)
(276,288)(289,307)(290,308)(291,309)(292,310)(293,311)(294,312)(295,301)
(296,302)(297,303)(298,304)(299,305)(300,306)(313,331)(314,332)(315,333)
(316,334)(317,335)(318,336)(319,325)(320,326)(321,327)(322,328)(323,329)
(324,330)(337,355)(338,356)(339,357)(340,358)(341,359)(342,360)(343,349)
(344,350)(345,351)(346,352)(347,353)(348,354)(361,379)(362,380)(363,381)
(364,382)(365,383)(366,384)(367,373)(368,374)(369,375)(370,376)(371,377)
(372,378);
s2 := Sym(384)!(  1,121)(  2,123)(  3,122)(  4,124)(  5,126)(  6,125)(  7,127)
(  8,129)(  9,128)( 10,130)( 11,132)( 12,131)( 13,133)( 14,135)( 15,134)
( 16,136)( 17,138)( 18,137)( 19,139)( 20,141)( 21,140)( 22,142)( 23,144)
( 24,143)( 25, 97)( 26, 99)( 27, 98)( 28,100)( 29,102)( 30,101)( 31,103)
( 32,105)( 33,104)( 34,106)( 35,108)( 36,107)( 37,109)( 38,111)( 39,110)
( 40,112)( 41,114)( 42,113)( 43,115)( 44,117)( 45,116)( 46,118)( 47,120)
( 48,119)( 49,172)( 50,174)( 51,173)( 52,169)( 53,171)( 54,170)( 55,178)
( 56,180)( 57,179)( 58,175)( 59,177)( 60,176)( 61,184)( 62,186)( 63,185)
( 64,181)( 65,183)( 66,182)( 67,190)( 68,192)( 69,191)( 70,187)( 71,189)
( 72,188)( 73,148)( 74,150)( 75,149)( 76,145)( 77,147)( 78,146)( 79,154)
( 80,156)( 81,155)( 82,151)( 83,153)( 84,152)( 85,160)( 86,162)( 87,161)
( 88,157)( 89,159)( 90,158)( 91,166)( 92,168)( 93,167)( 94,163)( 95,165)
( 96,164)(193,313)(194,315)(195,314)(196,316)(197,318)(198,317)(199,319)
(200,321)(201,320)(202,322)(203,324)(204,323)(205,325)(206,327)(207,326)
(208,328)(209,330)(210,329)(211,331)(212,333)(213,332)(214,334)(215,336)
(216,335)(217,289)(218,291)(219,290)(220,292)(221,294)(222,293)(223,295)
(224,297)(225,296)(226,298)(227,300)(228,299)(229,301)(230,303)(231,302)
(232,304)(233,306)(234,305)(235,307)(236,309)(237,308)(238,310)(239,312)
(240,311)(241,364)(242,366)(243,365)(244,361)(245,363)(246,362)(247,370)
(248,372)(249,371)(250,367)(251,369)(252,368)(253,376)(254,378)(255,377)
(256,373)(257,375)(258,374)(259,382)(260,384)(261,383)(262,379)(263,381)
(264,380)(265,340)(266,342)(267,341)(268,337)(269,339)(270,338)(271,346)
(272,348)(273,347)(274,343)(275,345)(276,344)(277,352)(278,354)(279,353)
(280,349)(281,351)(282,350)(283,358)(284,360)(285,359)(286,355)(287,357)
(288,356);
s3 := Sym(384)!(  1, 27)(  2, 26)(  3, 25)(  4, 30)(  5, 29)(  6, 28)(  7, 33)
(  8, 32)(  9, 31)( 10, 36)( 11, 35)( 12, 34)( 13, 39)( 14, 38)( 15, 37)
( 16, 42)( 17, 41)( 18, 40)( 19, 45)( 20, 44)( 21, 43)( 22, 48)( 23, 47)
( 24, 46)( 49, 75)( 50, 74)( 51, 73)( 52, 78)( 53, 77)( 54, 76)( 55, 81)
( 56, 80)( 57, 79)( 58, 84)( 59, 83)( 60, 82)( 61, 87)( 62, 86)( 63, 85)
( 64, 90)( 65, 89)( 66, 88)( 67, 93)( 68, 92)( 69, 91)( 70, 96)( 71, 95)
( 72, 94)( 97,123)( 98,122)( 99,121)(100,126)(101,125)(102,124)(103,129)
(104,128)(105,127)(106,132)(107,131)(108,130)(109,135)(110,134)(111,133)
(112,138)(113,137)(114,136)(115,141)(116,140)(117,139)(118,144)(119,143)
(120,142)(145,171)(146,170)(147,169)(148,174)(149,173)(150,172)(151,177)
(152,176)(153,175)(154,180)(155,179)(156,178)(157,183)(158,182)(159,181)
(160,186)(161,185)(162,184)(163,189)(164,188)(165,187)(166,192)(167,191)
(168,190)(193,219)(194,218)(195,217)(196,222)(197,221)(198,220)(199,225)
(200,224)(201,223)(202,228)(203,227)(204,226)(205,231)(206,230)(207,229)
(208,234)(209,233)(210,232)(211,237)(212,236)(213,235)(214,240)(215,239)
(216,238)(241,267)(242,266)(243,265)(244,270)(245,269)(246,268)(247,273)
(248,272)(249,271)(250,276)(251,275)(252,274)(253,279)(254,278)(255,277)
(256,282)(257,281)(258,280)(259,285)(260,284)(261,283)(262,288)(263,287)
(264,286)(289,315)(290,314)(291,313)(292,318)(293,317)(294,316)(295,321)
(296,320)(297,319)(298,324)(299,323)(300,322)(301,327)(302,326)(303,325)
(304,330)(305,329)(306,328)(307,333)(308,332)(309,331)(310,336)(311,335)
(312,334)(337,363)(338,362)(339,361)(340,366)(341,365)(342,364)(343,369)
(344,368)(345,367)(346,372)(347,371)(348,370)(349,375)(350,374)(351,373)
(352,378)(353,377)(354,376)(355,381)(356,380)(357,379)(358,384)(359,383)
(360,382);
s4 := Sym(384)!(  1, 49)(  2, 50)(  3, 51)(  4, 52)(  5, 53)(  6, 54)(  7, 55)
(  8, 56)(  9, 57)( 10, 58)( 11, 59)( 12, 60)( 13, 61)( 14, 62)( 15, 63)
( 16, 64)( 17, 65)( 18, 66)( 19, 67)( 20, 68)( 21, 69)( 22, 70)( 23, 71)
( 24, 72)( 25, 76)( 26, 77)( 27, 78)( 28, 73)( 29, 74)( 30, 75)( 31, 82)
( 32, 83)( 33, 84)( 34, 79)( 35, 80)( 36, 81)( 37, 88)( 38, 89)( 39, 90)
( 40, 85)( 41, 86)( 42, 87)( 43, 94)( 44, 95)( 45, 96)( 46, 91)( 47, 92)
( 48, 93)( 97,145)( 98,146)( 99,147)(100,148)(101,149)(102,150)(103,151)
(104,152)(105,153)(106,154)(107,155)(108,156)(109,157)(110,158)(111,159)
(112,160)(113,161)(114,162)(115,163)(116,164)(117,165)(118,166)(119,167)
(120,168)(121,172)(122,173)(123,174)(124,169)(125,170)(126,171)(127,178)
(128,179)(129,180)(130,175)(131,176)(132,177)(133,184)(134,185)(135,186)
(136,181)(137,182)(138,183)(139,190)(140,191)(141,192)(142,187)(143,188)
(144,189)(193,241)(194,242)(195,243)(196,244)(197,245)(198,246)(199,247)
(200,248)(201,249)(202,250)(203,251)(204,252)(205,253)(206,254)(207,255)
(208,256)(209,257)(210,258)(211,259)(212,260)(213,261)(214,262)(215,263)
(216,264)(217,268)(218,269)(219,270)(220,265)(221,266)(222,267)(223,274)
(224,275)(225,276)(226,271)(227,272)(228,273)(229,280)(230,281)(231,282)
(232,277)(233,278)(234,279)(235,286)(236,287)(237,288)(238,283)(239,284)
(240,285)(289,337)(290,338)(291,339)(292,340)(293,341)(294,342)(295,343)
(296,344)(297,345)(298,346)(299,347)(300,348)(301,349)(302,350)(303,351)
(304,352)(305,353)(306,354)(307,355)(308,356)(309,357)(310,358)(311,359)
(312,360)(313,364)(314,365)(315,366)(316,361)(317,362)(318,363)(319,370)
(320,371)(321,372)(322,367)(323,368)(324,369)(325,376)(326,377)(327,378)
(328,373)(329,374)(330,375)(331,382)(332,383)(333,384)(334,379)(335,380)
(336,381);
poly := sub<Sym(384)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 
References : None.
to this polytope