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