Polytope of Type {6,4,4,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,4,4}*768
Also Known As : {{6,4|2},{4,4|2},{4,4|2}}. if this polytope has another name.
Group : SmallGroup(768,336970)
Rank : 5
Schlafli Type : {6,4,4,4}
Number of vertices, edges, etc : 6, 12, 8, 8, 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 : {6,2,4,4}*384, {6,4,4,2}*384, {6,4,2,4}*384a
3-fold quotients : {2,4,4,4}*256
4-fold quotients : {3,2,4,4}*192, {6,2,2,4}*192, {6,2,4,2}*192, {6,4,2,2}*192a
6-fold quotients : {2,2,4,4}*128, {2,4,4,2}*128, {2,4,2,4}*128
8-fold quotients : {3,2,2,4}*96, {3,2,4,2}*96, {6,2,2,2}*96
12-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64, {2,4,2,2}*64
16-fold quotients : {3,2,2,2}*48
24-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 25)( 2, 27)( 3, 26)( 4, 28)( 5, 30)( 6, 29)( 7, 31)( 8, 33)
( 9, 32)( 10, 34)( 11, 36)( 12, 35)( 13, 37)( 14, 39)( 15, 38)( 16, 40)
( 17, 42)( 18, 41)( 19, 43)( 20, 45)( 21, 44)( 22, 46)( 23, 48)( 24, 47)
( 49, 73)( 50, 75)( 51, 74)( 52, 76)( 53, 78)( 54, 77)( 55, 79)( 56, 81)
( 57, 80)( 58, 82)( 59, 84)( 60, 83)( 61, 85)( 62, 87)( 63, 86)( 64, 88)
( 65, 90)( 66, 89)( 67, 91)( 68, 93)( 69, 92)( 70, 94)( 71, 96)( 72, 95)
( 97,121)( 98,123)( 99,122)(100,124)(101,126)(102,125)(103,127)(104,129)
(105,128)(106,130)(107,132)(108,131)(109,133)(110,135)(111,134)(112,136)
(113,138)(114,137)(115,139)(116,141)(117,140)(118,142)(119,144)(120,143)
(145,169)(146,171)(147,170)(148,172)(149,174)(150,173)(151,175)(152,177)
(153,176)(154,178)(155,180)(156,179)(157,181)(158,183)(159,182)(160,184)
(161,186)(162,185)(163,187)(164,189)(165,188)(166,190)(167,192)(168,191)
(193,217)(194,219)(195,218)(196,220)(197,222)(198,221)(199,223)(200,225)
(201,224)(202,226)(203,228)(204,227)(205,229)(206,231)(207,230)(208,232)
(209,234)(210,233)(211,235)(212,237)(213,236)(214,238)(215,240)(216,239)
(241,265)(242,267)(243,266)(244,268)(245,270)(246,269)(247,271)(248,273)
(249,272)(250,274)(251,276)(252,275)(253,277)(254,279)(255,278)(256,280)
(257,282)(258,281)(259,283)(260,285)(261,284)(262,286)(263,288)(264,287)
(289,313)(290,315)(291,314)(292,316)(293,318)(294,317)(295,319)(296,321)
(297,320)(298,322)(299,324)(300,323)(301,325)(302,327)(303,326)(304,328)
(305,330)(306,329)(307,331)(308,333)(309,332)(310,334)(311,336)(312,335)
(337,361)(338,363)(339,362)(340,364)(341,366)(342,365)(343,367)(344,369)
(345,368)(346,370)(347,372)(348,371)(349,373)(350,375)(351,374)(352,376)
(353,378)(354,377)(355,379)(356,381)(357,380)(358,382)(359,384)(360,383);;
s1 := ( 1, 75)( 2, 74)( 3, 73)( 4, 78)( 5, 77)( 6, 76)( 7, 81)( 8, 80)
( 9, 79)( 10, 84)( 11, 83)( 12, 82)( 13, 87)( 14, 86)( 15, 85)( 16, 90)
( 17, 89)( 18, 88)( 19, 93)( 20, 92)( 21, 91)( 22, 96)( 23, 95)( 24, 94)
( 25, 51)( 26, 50)( 27, 49)( 28, 54)( 29, 53)( 30, 52)( 31, 57)( 32, 56)
( 33, 55)( 34, 60)( 35, 59)( 36, 58)( 37, 63)( 38, 62)( 39, 61)( 40, 66)
( 41, 65)( 42, 64)( 43, 69)( 44, 68)( 45, 67)( 46, 72)( 47, 71)( 48, 70)
( 97,171)( 98,170)( 99,169)(100,174)(101,173)(102,172)(103,177)(104,176)
(105,175)(106,180)(107,179)(108,178)(109,183)(110,182)(111,181)(112,186)
(113,185)(114,184)(115,189)(116,188)(117,187)(118,192)(119,191)(120,190)
(121,147)(122,146)(123,145)(124,150)(125,149)(126,148)(127,153)(128,152)
(129,151)(130,156)(131,155)(132,154)(133,159)(134,158)(135,157)(136,162)
(137,161)(138,160)(139,165)(140,164)(141,163)(142,168)(143,167)(144,166)
(193,267)(194,266)(195,265)(196,270)(197,269)(198,268)(199,273)(200,272)
(201,271)(202,276)(203,275)(204,274)(205,279)(206,278)(207,277)(208,282)
(209,281)(210,280)(211,285)(212,284)(213,283)(214,288)(215,287)(216,286)
(217,243)(218,242)(219,241)(220,246)(221,245)(222,244)(223,249)(224,248)
(225,247)(226,252)(227,251)(228,250)(229,255)(230,254)(231,253)(232,258)
(233,257)(234,256)(235,261)(236,260)(237,259)(238,264)(239,263)(240,262)
(289,363)(290,362)(291,361)(292,366)(293,365)(294,364)(295,369)(296,368)
(297,367)(298,372)(299,371)(300,370)(301,375)(302,374)(303,373)(304,378)
(305,377)(306,376)(307,381)(308,380)(309,379)(310,384)(311,383)(312,382)
(313,339)(314,338)(315,337)(316,342)(317,341)(318,340)(319,345)(320,344)
(321,343)(322,348)(323,347)(324,346)(325,351)(326,350)(327,349)(328,354)
(329,353)(330,352)(331,357)(332,356)(333,355)(334,360)(335,359)(336,358);;
s2 := ( 1,193)( 2,194)( 3,195)( 4,196)( 5,197)( 6,198)( 7,199)( 8,200)
( 9,201)( 10,202)( 11,203)( 12,204)( 13,205)( 14,206)( 15,207)( 16,208)
( 17,209)( 18,210)( 19,211)( 20,212)( 21,213)( 22,214)( 23,215)( 24,216)
( 25,217)( 26,218)( 27,219)( 28,220)( 29,221)( 30,222)( 31,223)( 32,224)
( 33,225)( 34,226)( 35,227)( 36,228)( 37,229)( 38,230)( 39,231)( 40,232)
( 41,233)( 42,234)( 43,235)( 44,236)( 45,237)( 46,238)( 47,239)( 48,240)
( 49,244)( 50,245)( 51,246)( 52,241)( 53,242)( 54,243)( 55,250)( 56,251)
( 57,252)( 58,247)( 59,248)( 60,249)( 61,256)( 62,257)( 63,258)( 64,253)
( 65,254)( 66,255)( 67,262)( 68,263)( 69,264)( 70,259)( 71,260)( 72,261)
( 73,268)( 74,269)( 75,270)( 76,265)( 77,266)( 78,267)( 79,274)( 80,275)
( 81,276)( 82,271)( 83,272)( 84,273)( 85,280)( 86,281)( 87,282)( 88,277)
( 89,278)( 90,279)( 91,286)( 92,287)( 93,288)( 94,283)( 95,284)( 96,285)
( 97,292)( 98,293)( 99,294)(100,289)(101,290)(102,291)(103,298)(104,299)
(105,300)(106,295)(107,296)(108,297)(109,304)(110,305)(111,306)(112,301)
(113,302)(114,303)(115,310)(116,311)(117,312)(118,307)(119,308)(120,309)
(121,316)(122,317)(123,318)(124,313)(125,314)(126,315)(127,322)(128,323)
(129,324)(130,319)(131,320)(132,321)(133,328)(134,329)(135,330)(136,325)
(137,326)(138,327)(139,334)(140,335)(141,336)(142,331)(143,332)(144,333)
(145,337)(146,338)(147,339)(148,340)(149,341)(150,342)(151,343)(152,344)
(153,345)(154,346)(155,347)(156,348)(157,349)(158,350)(159,351)(160,352)
(161,353)(162,354)(163,355)(164,356)(165,357)(166,358)(167,359)(168,360)
(169,361)(170,362)(171,363)(172,364)(173,365)(174,366)(175,367)(176,368)
(177,369)(178,370)(179,371)(180,372)(181,373)(182,374)(183,375)(184,376)
(185,377)(186,378)(187,379)(188,380)(189,381)(190,382)(191,383)(192,384);;
s3 := ( 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);;
s4 := ( 1,145)( 2,146)( 3,147)( 4,148)( 5,149)( 6,150)( 7,151)( 8,152)
( 9,153)( 10,154)( 11,155)( 12,156)( 13,157)( 14,158)( 15,159)( 16,160)
( 17,161)( 18,162)( 19,163)( 20,164)( 21,165)( 22,166)( 23,167)( 24,168)
( 25,169)( 26,170)( 27,171)( 28,172)( 29,173)( 30,174)( 31,175)( 32,176)
( 33,177)( 34,178)( 35,179)( 36,180)( 37,181)( 38,182)( 39,183)( 40,184)
( 41,185)( 42,186)( 43,187)( 44,188)( 45,189)( 46,190)( 47,191)( 48,192)
( 49, 97)( 50, 98)( 51, 99)( 52,100)( 53,101)( 54,102)( 55,103)( 56,104)
( 57,105)( 58,106)( 59,107)( 60,108)( 61,109)( 62,110)( 63,111)( 64,112)
( 65,113)( 66,114)( 67,115)( 68,116)( 69,117)( 70,118)( 71,119)( 72,120)
( 73,121)( 74,122)( 75,123)( 76,124)( 77,125)( 78,126)( 79,127)( 80,128)
( 81,129)( 82,130)( 83,131)( 84,132)( 85,133)( 86,134)( 87,135)( 88,136)
( 89,137)( 90,138)( 91,139)( 92,140)( 93,141)( 94,142)( 95,143)( 96,144)
(193,337)(194,338)(195,339)(196,340)(197,341)(198,342)(199,343)(200,344)
(201,345)(202,346)(203,347)(204,348)(205,349)(206,350)(207,351)(208,352)
(209,353)(210,354)(211,355)(212,356)(213,357)(214,358)(215,359)(216,360)
(217,361)(218,362)(219,363)(220,364)(221,365)(222,366)(223,367)(224,368)
(225,369)(226,370)(227,371)(228,372)(229,373)(230,374)(231,375)(232,376)
(233,377)(234,378)(235,379)(236,380)(237,381)(238,382)(239,383)(240,384)
(241,289)(242,290)(243,291)(244,292)(245,293)(246,294)(247,295)(248,296)
(249,297)(250,298)(251,299)(252,300)(253,301)(254,302)(255,303)(256,304)
(257,305)(258,306)(259,307)(260,308)(261,309)(262,310)(263,311)(264,312)
(265,313)(266,314)(267,315)(268,316)(269,317)(270,318)(271,319)(272,320)
(273,321)(274,322)(275,323)(276,324)(277,325)(278,326)(279,327)(280,328)
(281,329)(282,330)(283,331)(284,332)(285,333)(286,334)(287,335)(288,336);;
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*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(384)!( 1, 25)( 2, 27)( 3, 26)( 4, 28)( 5, 30)( 6, 29)( 7, 31)
( 8, 33)( 9, 32)( 10, 34)( 11, 36)( 12, 35)( 13, 37)( 14, 39)( 15, 38)
( 16, 40)( 17, 42)( 18, 41)( 19, 43)( 20, 45)( 21, 44)( 22, 46)( 23, 48)
( 24, 47)( 49, 73)( 50, 75)( 51, 74)( 52, 76)( 53, 78)( 54, 77)( 55, 79)
( 56, 81)( 57, 80)( 58, 82)( 59, 84)( 60, 83)( 61, 85)( 62, 87)( 63, 86)
( 64, 88)( 65, 90)( 66, 89)( 67, 91)( 68, 93)( 69, 92)( 70, 94)( 71, 96)
( 72, 95)( 97,121)( 98,123)( 99,122)(100,124)(101,126)(102,125)(103,127)
(104,129)(105,128)(106,130)(107,132)(108,131)(109,133)(110,135)(111,134)
(112,136)(113,138)(114,137)(115,139)(116,141)(117,140)(118,142)(119,144)
(120,143)(145,169)(146,171)(147,170)(148,172)(149,174)(150,173)(151,175)
(152,177)(153,176)(154,178)(155,180)(156,179)(157,181)(158,183)(159,182)
(160,184)(161,186)(162,185)(163,187)(164,189)(165,188)(166,190)(167,192)
(168,191)(193,217)(194,219)(195,218)(196,220)(197,222)(198,221)(199,223)
(200,225)(201,224)(202,226)(203,228)(204,227)(205,229)(206,231)(207,230)
(208,232)(209,234)(210,233)(211,235)(212,237)(213,236)(214,238)(215,240)
(216,239)(241,265)(242,267)(243,266)(244,268)(245,270)(246,269)(247,271)
(248,273)(249,272)(250,274)(251,276)(252,275)(253,277)(254,279)(255,278)
(256,280)(257,282)(258,281)(259,283)(260,285)(261,284)(262,286)(263,288)
(264,287)(289,313)(290,315)(291,314)(292,316)(293,318)(294,317)(295,319)
(296,321)(297,320)(298,322)(299,324)(300,323)(301,325)(302,327)(303,326)
(304,328)(305,330)(306,329)(307,331)(308,333)(309,332)(310,334)(311,336)
(312,335)(337,361)(338,363)(339,362)(340,364)(341,366)(342,365)(343,367)
(344,369)(345,368)(346,370)(347,372)(348,371)(349,373)(350,375)(351,374)
(352,376)(353,378)(354,377)(355,379)(356,381)(357,380)(358,382)(359,384)
(360,383);
s1 := Sym(384)!( 1, 75)( 2, 74)( 3, 73)( 4, 78)( 5, 77)( 6, 76)( 7, 81)
( 8, 80)( 9, 79)( 10, 84)( 11, 83)( 12, 82)( 13, 87)( 14, 86)( 15, 85)
( 16, 90)( 17, 89)( 18, 88)( 19, 93)( 20, 92)( 21, 91)( 22, 96)( 23, 95)
( 24, 94)( 25, 51)( 26, 50)( 27, 49)( 28, 54)( 29, 53)( 30, 52)( 31, 57)
( 32, 56)( 33, 55)( 34, 60)( 35, 59)( 36, 58)( 37, 63)( 38, 62)( 39, 61)
( 40, 66)( 41, 65)( 42, 64)( 43, 69)( 44, 68)( 45, 67)( 46, 72)( 47, 71)
( 48, 70)( 97,171)( 98,170)( 99,169)(100,174)(101,173)(102,172)(103,177)
(104,176)(105,175)(106,180)(107,179)(108,178)(109,183)(110,182)(111,181)
(112,186)(113,185)(114,184)(115,189)(116,188)(117,187)(118,192)(119,191)
(120,190)(121,147)(122,146)(123,145)(124,150)(125,149)(126,148)(127,153)
(128,152)(129,151)(130,156)(131,155)(132,154)(133,159)(134,158)(135,157)
(136,162)(137,161)(138,160)(139,165)(140,164)(141,163)(142,168)(143,167)
(144,166)(193,267)(194,266)(195,265)(196,270)(197,269)(198,268)(199,273)
(200,272)(201,271)(202,276)(203,275)(204,274)(205,279)(206,278)(207,277)
(208,282)(209,281)(210,280)(211,285)(212,284)(213,283)(214,288)(215,287)
(216,286)(217,243)(218,242)(219,241)(220,246)(221,245)(222,244)(223,249)
(224,248)(225,247)(226,252)(227,251)(228,250)(229,255)(230,254)(231,253)
(232,258)(233,257)(234,256)(235,261)(236,260)(237,259)(238,264)(239,263)
(240,262)(289,363)(290,362)(291,361)(292,366)(293,365)(294,364)(295,369)
(296,368)(297,367)(298,372)(299,371)(300,370)(301,375)(302,374)(303,373)
(304,378)(305,377)(306,376)(307,381)(308,380)(309,379)(310,384)(311,383)
(312,382)(313,339)(314,338)(315,337)(316,342)(317,341)(318,340)(319,345)
(320,344)(321,343)(322,348)(323,347)(324,346)(325,351)(326,350)(327,349)
(328,354)(329,353)(330,352)(331,357)(332,356)(333,355)(334,360)(335,359)
(336,358);
s2 := Sym(384)!( 1,193)( 2,194)( 3,195)( 4,196)( 5,197)( 6,198)( 7,199)
( 8,200)( 9,201)( 10,202)( 11,203)( 12,204)( 13,205)( 14,206)( 15,207)
( 16,208)( 17,209)( 18,210)( 19,211)( 20,212)( 21,213)( 22,214)( 23,215)
( 24,216)( 25,217)( 26,218)( 27,219)( 28,220)( 29,221)( 30,222)( 31,223)
( 32,224)( 33,225)( 34,226)( 35,227)( 36,228)( 37,229)( 38,230)( 39,231)
( 40,232)( 41,233)( 42,234)( 43,235)( 44,236)( 45,237)( 46,238)( 47,239)
( 48,240)( 49,244)( 50,245)( 51,246)( 52,241)( 53,242)( 54,243)( 55,250)
( 56,251)( 57,252)( 58,247)( 59,248)( 60,249)( 61,256)( 62,257)( 63,258)
( 64,253)( 65,254)( 66,255)( 67,262)( 68,263)( 69,264)( 70,259)( 71,260)
( 72,261)( 73,268)( 74,269)( 75,270)( 76,265)( 77,266)( 78,267)( 79,274)
( 80,275)( 81,276)( 82,271)( 83,272)( 84,273)( 85,280)( 86,281)( 87,282)
( 88,277)( 89,278)( 90,279)( 91,286)( 92,287)( 93,288)( 94,283)( 95,284)
( 96,285)( 97,292)( 98,293)( 99,294)(100,289)(101,290)(102,291)(103,298)
(104,299)(105,300)(106,295)(107,296)(108,297)(109,304)(110,305)(111,306)
(112,301)(113,302)(114,303)(115,310)(116,311)(117,312)(118,307)(119,308)
(120,309)(121,316)(122,317)(123,318)(124,313)(125,314)(126,315)(127,322)
(128,323)(129,324)(130,319)(131,320)(132,321)(133,328)(134,329)(135,330)
(136,325)(137,326)(138,327)(139,334)(140,335)(141,336)(142,331)(143,332)
(144,333)(145,337)(146,338)(147,339)(148,340)(149,341)(150,342)(151,343)
(152,344)(153,345)(154,346)(155,347)(156,348)(157,349)(158,350)(159,351)
(160,352)(161,353)(162,354)(163,355)(164,356)(165,357)(166,358)(167,359)
(168,360)(169,361)(170,362)(171,363)(172,364)(173,365)(174,366)(175,367)
(176,368)(177,369)(178,370)(179,371)(180,372)(181,373)(182,374)(183,375)
(184,376)(185,377)(186,378)(187,379)(188,380)(189,381)(190,382)(191,383)
(192,384);
s3 := 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);
s4 := Sym(384)!( 1,145)( 2,146)( 3,147)( 4,148)( 5,149)( 6,150)( 7,151)
( 8,152)( 9,153)( 10,154)( 11,155)( 12,156)( 13,157)( 14,158)( 15,159)
( 16,160)( 17,161)( 18,162)( 19,163)( 20,164)( 21,165)( 22,166)( 23,167)
( 24,168)( 25,169)( 26,170)( 27,171)( 28,172)( 29,173)( 30,174)( 31,175)
( 32,176)( 33,177)( 34,178)( 35,179)( 36,180)( 37,181)( 38,182)( 39,183)
( 40,184)( 41,185)( 42,186)( 43,187)( 44,188)( 45,189)( 46,190)( 47,191)
( 48,192)( 49, 97)( 50, 98)( 51, 99)( 52,100)( 53,101)( 54,102)( 55,103)
( 56,104)( 57,105)( 58,106)( 59,107)( 60,108)( 61,109)( 62,110)( 63,111)
( 64,112)( 65,113)( 66,114)( 67,115)( 68,116)( 69,117)( 70,118)( 71,119)
( 72,120)( 73,121)( 74,122)( 75,123)( 76,124)( 77,125)( 78,126)( 79,127)
( 80,128)( 81,129)( 82,130)( 83,131)( 84,132)( 85,133)( 86,134)( 87,135)
( 88,136)( 89,137)( 90,138)( 91,139)( 92,140)( 93,141)( 94,142)( 95,143)
( 96,144)(193,337)(194,338)(195,339)(196,340)(197,341)(198,342)(199,343)
(200,344)(201,345)(202,346)(203,347)(204,348)(205,349)(206,350)(207,351)
(208,352)(209,353)(210,354)(211,355)(212,356)(213,357)(214,358)(215,359)
(216,360)(217,361)(218,362)(219,363)(220,364)(221,365)(222,366)(223,367)
(224,368)(225,369)(226,370)(227,371)(228,372)(229,373)(230,374)(231,375)
(232,376)(233,377)(234,378)(235,379)(236,380)(237,381)(238,382)(239,383)
(240,384)(241,289)(242,290)(243,291)(244,292)(245,293)(246,294)(247,295)
(248,296)(249,297)(250,298)(251,299)(252,300)(253,301)(254,302)(255,303)
(256,304)(257,305)(258,306)(259,307)(260,308)(261,309)(262,310)(263,311)
(264,312)(265,313)(266,314)(267,315)(268,316)(269,317)(270,318)(271,319)
(272,320)(273,321)(274,322)(275,323)(276,324)(277,325)(278,326)(279,327)
(280,328)(281,329)(282,330)(283,331)(284,332)(285,333)(286,334)(287,335)
(288,336);
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*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope