Questions?
See the FAQ
or other info.

# Polytope of Type {4,6,6}

Atlas Canonical Name : {4,6,6}*1728b
if this polytope has a name.
Group : SmallGroup(1728,46116)
Rank : 4
Schlafli Type : {4,6,6}
Number of vertices, edges, etc : 8, 72, 108, 18
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
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 : {4,6,6}*864e, {4,6,6}*864g
3-fold quotients : {4,6,6}*576a
4-fold quotients : {4,6,6}*432, {2,6,6}*432b
6-fold quotients : {4,6,6}*288d
8-fold quotients : {2,6,6}*216
9-fold quotients : {4,6,2}*192
12-fold quotients : {2,6,6}*144a
18-fold quotients : {4,3,2}*96, {4,6,2}*96b, {4,6,2}*96c
36-fold quotients : {4,3,2}*48, {2,2,6}*48, {2,6,2}*48
72-fold quotients : {2,2,3}*24, {2,3,2}*24
108-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (  1,219)(  2,220)(  3,217)(  4,218)(  5,223)(  6,224)(  7,221)(  8,222)
(  9,227)( 10,228)( 11,225)( 12,226)( 13,231)( 14,232)( 15,229)( 16,230)
( 17,235)( 18,236)( 19,233)( 20,234)( 21,239)( 22,240)( 23,237)( 24,238)
( 25,243)( 26,244)( 27,241)( 28,242)( 29,247)( 30,248)( 31,245)( 32,246)
( 33,251)( 34,252)( 35,249)( 36,250)( 37,255)( 38,256)( 39,253)( 40,254)
( 41,259)( 42,260)( 43,257)( 44,258)( 45,263)( 46,264)( 47,261)( 48,262)
( 49,267)( 50,268)( 51,265)( 52,266)( 53,271)( 54,272)( 55,269)( 56,270)
( 57,275)( 58,276)( 59,273)( 60,274)( 61,279)( 62,280)( 63,277)( 64,278)
( 65,283)( 66,284)( 67,281)( 68,282)( 69,287)( 70,288)( 71,285)( 72,286)
( 73,291)( 74,292)( 75,289)( 76,290)( 77,295)( 78,296)( 79,293)( 80,294)
( 81,299)( 82,300)( 83,297)( 84,298)( 85,303)( 86,304)( 87,301)( 88,302)
( 89,307)( 90,308)( 91,305)( 92,306)( 93,311)( 94,312)( 95,309)( 96,310)
( 97,315)( 98,316)( 99,313)(100,314)(101,319)(102,320)(103,317)(104,318)
(105,323)(106,324)(107,321)(108,322)(109,327)(110,328)(111,325)(112,326)
(113,331)(114,332)(115,329)(116,330)(117,335)(118,336)(119,333)(120,334)
(121,339)(122,340)(123,337)(124,338)(125,343)(126,344)(127,341)(128,342)
(129,347)(130,348)(131,345)(132,346)(133,351)(134,352)(135,349)(136,350)
(137,355)(138,356)(139,353)(140,354)(141,359)(142,360)(143,357)(144,358)
(145,363)(146,364)(147,361)(148,362)(149,367)(150,368)(151,365)(152,366)
(153,371)(154,372)(155,369)(156,370)(157,375)(158,376)(159,373)(160,374)
(161,379)(162,380)(163,377)(164,378)(165,383)(166,384)(167,381)(168,382)
(169,387)(170,388)(171,385)(172,386)(173,391)(174,392)(175,389)(176,390)
(177,395)(178,396)(179,393)(180,394)(181,399)(182,400)(183,397)(184,398)
(185,403)(186,404)(187,401)(188,402)(189,407)(190,408)(191,405)(192,406)
(193,411)(194,412)(195,409)(196,410)(197,415)(198,416)(199,413)(200,414)
(201,419)(202,420)(203,417)(204,418)(205,423)(206,424)(207,421)(208,422)
(209,427)(210,428)(211,425)(212,426)(213,431)(214,432)(215,429)(216,430);;
s1 := (  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 15, 16)( 17, 21)( 18, 22)
( 19, 24)( 20, 23)( 27, 28)( 29, 33)( 30, 34)( 31, 36)( 32, 35)( 37, 73)
( 38, 74)( 39, 76)( 40, 75)( 41, 81)( 42, 82)( 43, 84)( 44, 83)( 45, 77)
( 46, 78)( 47, 80)( 48, 79)( 49, 85)( 50, 86)( 51, 88)( 52, 87)( 53, 93)
( 54, 94)( 55, 96)( 56, 95)( 57, 89)( 58, 90)( 59, 92)( 60, 91)( 61, 97)
( 62, 98)( 63,100)( 64, 99)( 65,105)( 66,106)( 67,108)( 68,107)( 69,101)
( 70,102)( 71,104)( 72,103)(111,112)(113,117)(114,118)(115,120)(116,119)
(123,124)(125,129)(126,130)(127,132)(128,131)(135,136)(137,141)(138,142)
(139,144)(140,143)(145,181)(146,182)(147,184)(148,183)(149,189)(150,190)
(151,192)(152,191)(153,185)(154,186)(155,188)(156,187)(157,193)(158,194)
(159,196)(160,195)(161,201)(162,202)(163,204)(164,203)(165,197)(166,198)
(167,200)(168,199)(169,205)(170,206)(171,208)(172,207)(173,213)(174,214)
(175,216)(176,215)(177,209)(178,210)(179,212)(180,211)(219,220)(221,225)
(222,226)(223,228)(224,227)(231,232)(233,237)(234,238)(235,240)(236,239)
(243,244)(245,249)(246,250)(247,252)(248,251)(253,289)(254,290)(255,292)
(256,291)(257,297)(258,298)(259,300)(260,299)(261,293)(262,294)(263,296)
(264,295)(265,301)(266,302)(267,304)(268,303)(269,309)(270,310)(271,312)
(272,311)(273,305)(274,306)(275,308)(276,307)(277,313)(278,314)(279,316)
(280,315)(281,321)(282,322)(283,324)(284,323)(285,317)(286,318)(287,320)
(288,319)(327,328)(329,333)(330,334)(331,336)(332,335)(339,340)(341,345)
(342,346)(343,348)(344,347)(351,352)(353,357)(354,358)(355,360)(356,359)
(361,397)(362,398)(363,400)(364,399)(365,405)(366,406)(367,408)(368,407)
(369,401)(370,402)(371,404)(372,403)(373,409)(374,410)(375,412)(376,411)
(377,417)(378,418)(379,420)(380,419)(381,413)(382,414)(383,416)(384,415)
(385,421)(386,422)(387,424)(388,423)(389,429)(390,430)(391,432)(392,431)
(393,425)(394,426)(395,428)(396,427);;
s2 := (  1, 37)(  2, 40)(  3, 39)(  4, 38)(  5, 41)(  6, 44)(  7, 43)(  8, 42)
(  9, 45)( 10, 48)( 11, 47)( 12, 46)( 13, 69)( 14, 72)( 15, 71)( 16, 70)
( 17, 61)( 18, 64)( 19, 63)( 20, 62)( 21, 65)( 22, 68)( 23, 67)( 24, 66)
( 25, 53)( 26, 56)( 27, 55)( 28, 54)( 29, 57)( 30, 60)( 31, 59)( 32, 58)
( 33, 49)( 34, 52)( 35, 51)( 36, 50)( 74, 76)( 78, 80)( 82, 84)( 85,105)
( 86,108)( 87,107)( 88,106)( 89, 97)( 90,100)( 91, 99)( 92, 98)( 93,101)
( 94,104)( 95,103)( 96,102)(109,145)(110,148)(111,147)(112,146)(113,149)
(114,152)(115,151)(116,150)(117,153)(118,156)(119,155)(120,154)(121,177)
(122,180)(123,179)(124,178)(125,169)(126,172)(127,171)(128,170)(129,173)
(130,176)(131,175)(132,174)(133,161)(134,164)(135,163)(136,162)(137,165)
(138,168)(139,167)(140,166)(141,157)(142,160)(143,159)(144,158)(182,184)
(186,188)(190,192)(193,213)(194,216)(195,215)(196,214)(197,205)(198,208)
(199,207)(200,206)(201,209)(202,212)(203,211)(204,210)(217,253)(218,256)
(219,255)(220,254)(221,257)(222,260)(223,259)(224,258)(225,261)(226,264)
(227,263)(228,262)(229,285)(230,288)(231,287)(232,286)(233,277)(234,280)
(235,279)(236,278)(237,281)(238,284)(239,283)(240,282)(241,269)(242,272)
(243,271)(244,270)(245,273)(246,276)(247,275)(248,274)(249,265)(250,268)
(251,267)(252,266)(290,292)(294,296)(298,300)(301,321)(302,324)(303,323)
(304,322)(305,313)(306,316)(307,315)(308,314)(309,317)(310,320)(311,319)
(312,318)(325,361)(326,364)(327,363)(328,362)(329,365)(330,368)(331,367)
(332,366)(333,369)(334,372)(335,371)(336,370)(337,393)(338,396)(339,395)
(340,394)(341,385)(342,388)(343,387)(344,386)(345,389)(346,392)(347,391)
(348,390)(349,377)(350,380)(351,379)(352,378)(353,381)(354,384)(355,383)
(356,382)(357,373)(358,376)(359,375)(360,374)(398,400)(402,404)(406,408)
(409,429)(410,432)(411,431)(412,430)(413,421)(414,424)(415,423)(416,422)
(417,425)(418,428)(419,427)(420,426);;
s3 := (  1,121)(  2,122)(  3,123)(  4,124)(  5,129)(  6,130)(  7,131)(  8,132)
(  9,125)( 10,126)( 11,127)( 12,128)( 13,109)( 14,110)( 15,111)( 16,112)
( 17,117)( 18,118)( 19,119)( 20,120)( 21,113)( 22,114)( 23,115)( 24,116)
( 25,133)( 26,134)( 27,135)( 28,136)( 29,141)( 30,142)( 31,143)( 32,144)
( 33,137)( 34,138)( 35,139)( 36,140)( 37,157)( 38,158)( 39,159)( 40,160)
( 41,165)( 42,166)( 43,167)( 44,168)( 45,161)( 46,162)( 47,163)( 48,164)
( 49,145)( 50,146)( 51,147)( 52,148)( 53,153)( 54,154)( 55,155)( 56,156)
( 57,149)( 58,150)( 59,151)( 60,152)( 61,169)( 62,170)( 63,171)( 64,172)
( 65,177)( 66,178)( 67,179)( 68,180)( 69,173)( 70,174)( 71,175)( 72,176)
( 73,193)( 74,194)( 75,195)( 76,196)( 77,201)( 78,202)( 79,203)( 80,204)
( 81,197)( 82,198)( 83,199)( 84,200)( 85,181)( 86,182)( 87,183)( 88,184)
( 89,189)( 90,190)( 91,191)( 92,192)( 93,185)( 94,186)( 95,187)( 96,188)
( 97,205)( 98,206)( 99,207)(100,208)(101,213)(102,214)(103,215)(104,216)
(105,209)(106,210)(107,211)(108,212)(217,337)(218,338)(219,339)(220,340)
(221,345)(222,346)(223,347)(224,348)(225,341)(226,342)(227,343)(228,344)
(229,325)(230,326)(231,327)(232,328)(233,333)(234,334)(235,335)(236,336)
(237,329)(238,330)(239,331)(240,332)(241,349)(242,350)(243,351)(244,352)
(245,357)(246,358)(247,359)(248,360)(249,353)(250,354)(251,355)(252,356)
(253,373)(254,374)(255,375)(256,376)(257,381)(258,382)(259,383)(260,384)
(261,377)(262,378)(263,379)(264,380)(265,361)(266,362)(267,363)(268,364)
(269,369)(270,370)(271,371)(272,372)(273,365)(274,366)(275,367)(276,368)
(277,385)(278,386)(279,387)(280,388)(281,393)(282,394)(283,395)(284,396)
(285,389)(286,390)(287,391)(288,392)(289,409)(290,410)(291,411)(292,412)
(293,417)(294,418)(295,419)(296,420)(297,413)(298,414)(299,415)(300,416)
(301,397)(302,398)(303,399)(304,400)(305,405)(306,406)(307,407)(308,408)
(309,401)(310,402)(311,403)(312,404)(313,421)(314,422)(315,423)(316,424)
(317,429)(318,430)(319,431)(320,432)(321,425)(322,426)(323,427)(324,428);;
poly := Group([s0,s1,s2,s3]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(432)!(  1,219)(  2,220)(  3,217)(  4,218)(  5,223)(  6,224)(  7,221)
(  8,222)(  9,227)( 10,228)( 11,225)( 12,226)( 13,231)( 14,232)( 15,229)
( 16,230)( 17,235)( 18,236)( 19,233)( 20,234)( 21,239)( 22,240)( 23,237)
( 24,238)( 25,243)( 26,244)( 27,241)( 28,242)( 29,247)( 30,248)( 31,245)
( 32,246)( 33,251)( 34,252)( 35,249)( 36,250)( 37,255)( 38,256)( 39,253)
( 40,254)( 41,259)( 42,260)( 43,257)( 44,258)( 45,263)( 46,264)( 47,261)
( 48,262)( 49,267)( 50,268)( 51,265)( 52,266)( 53,271)( 54,272)( 55,269)
( 56,270)( 57,275)( 58,276)( 59,273)( 60,274)( 61,279)( 62,280)( 63,277)
( 64,278)( 65,283)( 66,284)( 67,281)( 68,282)( 69,287)( 70,288)( 71,285)
( 72,286)( 73,291)( 74,292)( 75,289)( 76,290)( 77,295)( 78,296)( 79,293)
( 80,294)( 81,299)( 82,300)( 83,297)( 84,298)( 85,303)( 86,304)( 87,301)
( 88,302)( 89,307)( 90,308)( 91,305)( 92,306)( 93,311)( 94,312)( 95,309)
( 96,310)( 97,315)( 98,316)( 99,313)(100,314)(101,319)(102,320)(103,317)
(104,318)(105,323)(106,324)(107,321)(108,322)(109,327)(110,328)(111,325)
(112,326)(113,331)(114,332)(115,329)(116,330)(117,335)(118,336)(119,333)
(120,334)(121,339)(122,340)(123,337)(124,338)(125,343)(126,344)(127,341)
(128,342)(129,347)(130,348)(131,345)(132,346)(133,351)(134,352)(135,349)
(136,350)(137,355)(138,356)(139,353)(140,354)(141,359)(142,360)(143,357)
(144,358)(145,363)(146,364)(147,361)(148,362)(149,367)(150,368)(151,365)
(152,366)(153,371)(154,372)(155,369)(156,370)(157,375)(158,376)(159,373)
(160,374)(161,379)(162,380)(163,377)(164,378)(165,383)(166,384)(167,381)
(168,382)(169,387)(170,388)(171,385)(172,386)(173,391)(174,392)(175,389)
(176,390)(177,395)(178,396)(179,393)(180,394)(181,399)(182,400)(183,397)
(184,398)(185,403)(186,404)(187,401)(188,402)(189,407)(190,408)(191,405)
(192,406)(193,411)(194,412)(195,409)(196,410)(197,415)(198,416)(199,413)
(200,414)(201,419)(202,420)(203,417)(204,418)(205,423)(206,424)(207,421)
(208,422)(209,427)(210,428)(211,425)(212,426)(213,431)(214,432)(215,429)
(216,430);
s1 := Sym(432)!(  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 15, 16)( 17, 21)
( 18, 22)( 19, 24)( 20, 23)( 27, 28)( 29, 33)( 30, 34)( 31, 36)( 32, 35)
( 37, 73)( 38, 74)( 39, 76)( 40, 75)( 41, 81)( 42, 82)( 43, 84)( 44, 83)
( 45, 77)( 46, 78)( 47, 80)( 48, 79)( 49, 85)( 50, 86)( 51, 88)( 52, 87)
( 53, 93)( 54, 94)( 55, 96)( 56, 95)( 57, 89)( 58, 90)( 59, 92)( 60, 91)
( 61, 97)( 62, 98)( 63,100)( 64, 99)( 65,105)( 66,106)( 67,108)( 68,107)
( 69,101)( 70,102)( 71,104)( 72,103)(111,112)(113,117)(114,118)(115,120)
(116,119)(123,124)(125,129)(126,130)(127,132)(128,131)(135,136)(137,141)
(138,142)(139,144)(140,143)(145,181)(146,182)(147,184)(148,183)(149,189)
(150,190)(151,192)(152,191)(153,185)(154,186)(155,188)(156,187)(157,193)
(158,194)(159,196)(160,195)(161,201)(162,202)(163,204)(164,203)(165,197)
(166,198)(167,200)(168,199)(169,205)(170,206)(171,208)(172,207)(173,213)
(174,214)(175,216)(176,215)(177,209)(178,210)(179,212)(180,211)(219,220)
(221,225)(222,226)(223,228)(224,227)(231,232)(233,237)(234,238)(235,240)
(236,239)(243,244)(245,249)(246,250)(247,252)(248,251)(253,289)(254,290)
(255,292)(256,291)(257,297)(258,298)(259,300)(260,299)(261,293)(262,294)
(263,296)(264,295)(265,301)(266,302)(267,304)(268,303)(269,309)(270,310)
(271,312)(272,311)(273,305)(274,306)(275,308)(276,307)(277,313)(278,314)
(279,316)(280,315)(281,321)(282,322)(283,324)(284,323)(285,317)(286,318)
(287,320)(288,319)(327,328)(329,333)(330,334)(331,336)(332,335)(339,340)
(341,345)(342,346)(343,348)(344,347)(351,352)(353,357)(354,358)(355,360)
(356,359)(361,397)(362,398)(363,400)(364,399)(365,405)(366,406)(367,408)
(368,407)(369,401)(370,402)(371,404)(372,403)(373,409)(374,410)(375,412)
(376,411)(377,417)(378,418)(379,420)(380,419)(381,413)(382,414)(383,416)
(384,415)(385,421)(386,422)(387,424)(388,423)(389,429)(390,430)(391,432)
(392,431)(393,425)(394,426)(395,428)(396,427);
s2 := Sym(432)!(  1, 37)(  2, 40)(  3, 39)(  4, 38)(  5, 41)(  6, 44)(  7, 43)
(  8, 42)(  9, 45)( 10, 48)( 11, 47)( 12, 46)( 13, 69)( 14, 72)( 15, 71)
( 16, 70)( 17, 61)( 18, 64)( 19, 63)( 20, 62)( 21, 65)( 22, 68)( 23, 67)
( 24, 66)( 25, 53)( 26, 56)( 27, 55)( 28, 54)( 29, 57)( 30, 60)( 31, 59)
( 32, 58)( 33, 49)( 34, 52)( 35, 51)( 36, 50)( 74, 76)( 78, 80)( 82, 84)
( 85,105)( 86,108)( 87,107)( 88,106)( 89, 97)( 90,100)( 91, 99)( 92, 98)
( 93,101)( 94,104)( 95,103)( 96,102)(109,145)(110,148)(111,147)(112,146)
(113,149)(114,152)(115,151)(116,150)(117,153)(118,156)(119,155)(120,154)
(121,177)(122,180)(123,179)(124,178)(125,169)(126,172)(127,171)(128,170)
(129,173)(130,176)(131,175)(132,174)(133,161)(134,164)(135,163)(136,162)
(137,165)(138,168)(139,167)(140,166)(141,157)(142,160)(143,159)(144,158)
(182,184)(186,188)(190,192)(193,213)(194,216)(195,215)(196,214)(197,205)
(198,208)(199,207)(200,206)(201,209)(202,212)(203,211)(204,210)(217,253)
(218,256)(219,255)(220,254)(221,257)(222,260)(223,259)(224,258)(225,261)
(226,264)(227,263)(228,262)(229,285)(230,288)(231,287)(232,286)(233,277)
(234,280)(235,279)(236,278)(237,281)(238,284)(239,283)(240,282)(241,269)
(242,272)(243,271)(244,270)(245,273)(246,276)(247,275)(248,274)(249,265)
(250,268)(251,267)(252,266)(290,292)(294,296)(298,300)(301,321)(302,324)
(303,323)(304,322)(305,313)(306,316)(307,315)(308,314)(309,317)(310,320)
(311,319)(312,318)(325,361)(326,364)(327,363)(328,362)(329,365)(330,368)
(331,367)(332,366)(333,369)(334,372)(335,371)(336,370)(337,393)(338,396)
(339,395)(340,394)(341,385)(342,388)(343,387)(344,386)(345,389)(346,392)
(347,391)(348,390)(349,377)(350,380)(351,379)(352,378)(353,381)(354,384)
(355,383)(356,382)(357,373)(358,376)(359,375)(360,374)(398,400)(402,404)
(406,408)(409,429)(410,432)(411,431)(412,430)(413,421)(414,424)(415,423)
(416,422)(417,425)(418,428)(419,427)(420,426);
s3 := Sym(432)!(  1,121)(  2,122)(  3,123)(  4,124)(  5,129)(  6,130)(  7,131)
(  8,132)(  9,125)( 10,126)( 11,127)( 12,128)( 13,109)( 14,110)( 15,111)
( 16,112)( 17,117)( 18,118)( 19,119)( 20,120)( 21,113)( 22,114)( 23,115)
( 24,116)( 25,133)( 26,134)( 27,135)( 28,136)( 29,141)( 30,142)( 31,143)
( 32,144)( 33,137)( 34,138)( 35,139)( 36,140)( 37,157)( 38,158)( 39,159)
( 40,160)( 41,165)( 42,166)( 43,167)( 44,168)( 45,161)( 46,162)( 47,163)
( 48,164)( 49,145)( 50,146)( 51,147)( 52,148)( 53,153)( 54,154)( 55,155)
( 56,156)( 57,149)( 58,150)( 59,151)( 60,152)( 61,169)( 62,170)( 63,171)
( 64,172)( 65,177)( 66,178)( 67,179)( 68,180)( 69,173)( 70,174)( 71,175)
( 72,176)( 73,193)( 74,194)( 75,195)( 76,196)( 77,201)( 78,202)( 79,203)
( 80,204)( 81,197)( 82,198)( 83,199)( 84,200)( 85,181)( 86,182)( 87,183)
( 88,184)( 89,189)( 90,190)( 91,191)( 92,192)( 93,185)( 94,186)( 95,187)
( 96,188)( 97,205)( 98,206)( 99,207)(100,208)(101,213)(102,214)(103,215)
(104,216)(105,209)(106,210)(107,211)(108,212)(217,337)(218,338)(219,339)
(220,340)(221,345)(222,346)(223,347)(224,348)(225,341)(226,342)(227,343)
(228,344)(229,325)(230,326)(231,327)(232,328)(233,333)(234,334)(235,335)
(236,336)(237,329)(238,330)(239,331)(240,332)(241,349)(242,350)(243,351)
(244,352)(245,357)(246,358)(247,359)(248,360)(249,353)(250,354)(251,355)
(252,356)(253,373)(254,374)(255,375)(256,376)(257,381)(258,382)(259,383)
(260,384)(261,377)(262,378)(263,379)(264,380)(265,361)(266,362)(267,363)
(268,364)(269,369)(270,370)(271,371)(272,372)(273,365)(274,366)(275,367)
(276,368)(277,385)(278,386)(279,387)(280,388)(281,393)(282,394)(283,395)
(284,396)(285,389)(286,390)(287,391)(288,392)(289,409)(290,410)(291,411)
(292,412)(293,417)(294,418)(295,419)(296,420)(297,413)(298,414)(299,415)
(300,416)(301,397)(302,398)(303,399)(304,400)(305,405)(306,406)(307,407)
(308,408)(309,401)(310,402)(311,403)(312,404)(313,421)(314,422)(315,423)
(316,424)(317,429)(318,430)(319,431)(320,432)(321,425)(322,426)(323,427)
(324,428);
poly := sub<Sym(432)|s0,s1,s2,s3>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s2 >;

```
References : None.
to this polytope