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