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# Polytope of Type {3,6,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,24}*864b
if this polytope has a name.
Group : SmallGroup(864,2800)
Rank : 4
Schlafli Type : {3,6,24}
Number of vertices, edges, etc : 3, 9, 72, 24
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,6,24,2} of size 1728
Vertex Figure Of :
{2,3,6,24} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,6,12}*432b
3-fold quotients : {3,2,24}*288, {3,6,8}*288
4-fold quotients : {3,6,6}*216b
6-fold quotients : {3,2,12}*144, {3,6,4}*144
9-fold quotients : {3,2,8}*96
12-fold quotients : {3,2,6}*72, {3,6,2}*72
18-fold quotients : {3,2,4}*48
24-fold quotients : {3,2,3}*36
36-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,6,48}*1728b, {6,6,24}*1728e
Permutation Representation (GAP) :
```s0 := (  1,379)(  2,380)(  3,381)(  4,385)(  5,386)(  6,387)(  7,382)(  8,383)
(  9,384)( 10,397)( 11,398)( 12,399)( 13,403)( 14,404)( 15,405)( 16,400)
( 17,401)( 18,402)( 19,388)( 20,389)( 21,390)( 22,394)( 23,395)( 24,396)
( 25,391)( 26,392)( 27,393)( 28,406)( 29,407)( 30,408)( 31,412)( 32,413)
( 33,414)( 34,409)( 35,410)( 36,411)( 37,424)( 38,425)( 39,426)( 40,430)
( 41,431)( 42,432)( 43,427)( 44,428)( 45,429)( 46,415)( 47,416)( 48,417)
( 49,421)( 50,422)( 51,423)( 52,418)( 53,419)( 54,420)( 55,352)( 56,353)
( 57,354)( 58,358)( 59,359)( 60,360)( 61,355)( 62,356)( 63,357)( 64,370)
( 65,371)( 66,372)( 67,376)( 68,377)( 69,378)( 70,373)( 71,374)( 72,375)
( 73,361)( 74,362)( 75,363)( 76,367)( 77,368)( 78,369)( 79,364)( 80,365)
( 81,366)( 82,325)( 83,326)( 84,327)( 85,331)( 86,332)( 87,333)( 88,328)
( 89,329)( 90,330)( 91,343)( 92,344)( 93,345)( 94,349)( 95,350)( 96,351)
( 97,346)( 98,347)( 99,348)(100,334)(101,335)(102,336)(103,340)(104,341)
(105,342)(106,337)(107,338)(108,339)(109,217)(110,218)(111,219)(112,223)
(113,224)(114,225)(115,220)(116,221)(117,222)(118,235)(119,236)(120,237)
(121,241)(122,242)(123,243)(124,238)(125,239)(126,240)(127,226)(128,227)
(129,228)(130,232)(131,233)(132,234)(133,229)(134,230)(135,231)(136,244)
(137,245)(138,246)(139,250)(140,251)(141,252)(142,247)(143,248)(144,249)
(145,262)(146,263)(147,264)(148,268)(149,269)(150,270)(151,265)(152,266)
(153,267)(154,253)(155,254)(156,255)(157,259)(158,260)(159,261)(160,256)
(161,257)(162,258)(163,271)(164,272)(165,273)(166,277)(167,278)(168,279)
(169,274)(170,275)(171,276)(172,289)(173,290)(174,291)(175,295)(176,296)
(177,297)(178,292)(179,293)(180,294)(181,280)(182,281)(183,282)(184,286)
(185,287)(186,288)(187,283)(188,284)(189,285)(190,298)(191,299)(192,300)
(193,304)(194,305)(195,306)(196,301)(197,302)(198,303)(199,316)(200,317)
(201,318)(202,322)(203,323)(204,324)(205,319)(206,320)(207,321)(208,307)
(209,308)(210,309)(211,313)(212,314)(213,315)(214,310)(215,311)(216,312);;
s1 := (  1,391)(  2,392)(  3,393)(  4,388)(  5,389)(  6,390)(  7,394)(  8,395)
(  9,396)( 10,382)( 11,383)( 12,384)( 13,379)( 14,380)( 15,381)( 16,385)
( 17,386)( 18,387)( 19,400)( 20,401)( 21,402)( 22,397)( 23,398)( 24,399)
( 25,403)( 26,404)( 27,405)( 28,418)( 29,419)( 30,420)( 31,415)( 32,416)
( 33,417)( 34,421)( 35,422)( 36,423)( 37,409)( 38,410)( 39,411)( 40,406)
( 41,407)( 42,408)( 43,412)( 44,413)( 45,414)( 46,427)( 47,428)( 48,429)
( 49,424)( 50,425)( 51,426)( 52,430)( 53,431)( 54,432)( 55,364)( 56,365)
( 57,366)( 58,361)( 59,362)( 60,363)( 61,367)( 62,368)( 63,369)( 64,355)
( 65,356)( 66,357)( 67,352)( 68,353)( 69,354)( 70,358)( 71,359)( 72,360)
( 73,373)( 74,374)( 75,375)( 76,370)( 77,371)( 78,372)( 79,376)( 80,377)
( 81,378)( 82,337)( 83,338)( 84,339)( 85,334)( 86,335)( 87,336)( 88,340)
( 89,341)( 90,342)( 91,328)( 92,329)( 93,330)( 94,325)( 95,326)( 96,327)
( 97,331)( 98,332)( 99,333)(100,346)(101,347)(102,348)(103,343)(104,344)
(105,345)(106,349)(107,350)(108,351)(109,229)(110,230)(111,231)(112,226)
(113,227)(114,228)(115,232)(116,233)(117,234)(118,220)(119,221)(120,222)
(121,217)(122,218)(123,219)(124,223)(125,224)(126,225)(127,238)(128,239)
(129,240)(130,235)(131,236)(132,237)(133,241)(134,242)(135,243)(136,256)
(137,257)(138,258)(139,253)(140,254)(141,255)(142,259)(143,260)(144,261)
(145,247)(146,248)(147,249)(148,244)(149,245)(150,246)(151,250)(152,251)
(153,252)(154,265)(155,266)(156,267)(157,262)(158,263)(159,264)(160,268)
(161,269)(162,270)(163,283)(164,284)(165,285)(166,280)(167,281)(168,282)
(169,286)(170,287)(171,288)(172,274)(173,275)(174,276)(175,271)(176,272)
(177,273)(178,277)(179,278)(180,279)(181,292)(182,293)(183,294)(184,289)
(185,290)(186,291)(187,295)(188,296)(189,297)(190,310)(191,311)(192,312)
(193,307)(194,308)(195,309)(196,313)(197,314)(198,315)(199,301)(200,302)
(201,303)(202,298)(203,299)(204,300)(205,304)(206,305)(207,306)(208,319)
(209,320)(210,321)(211,316)(212,317)(213,318)(214,322)(215,323)(216,324);;
s2 := (  1,217)(  2,219)(  3,218)(  4,223)(  5,225)(  6,224)(  7,220)(  8,222)
(  9,221)( 10,226)( 11,228)( 12,227)( 13,232)( 14,234)( 15,233)( 16,229)
( 17,231)( 18,230)( 19,235)( 20,237)( 21,236)( 22,241)( 23,243)( 24,242)
( 25,238)( 26,240)( 27,239)( 28,244)( 29,246)( 30,245)( 31,250)( 32,252)
( 33,251)( 34,247)( 35,249)( 36,248)( 37,253)( 38,255)( 39,254)( 40,259)
( 41,261)( 42,260)( 43,256)( 44,258)( 45,257)( 46,262)( 47,264)( 48,263)
( 49,268)( 50,270)( 51,269)( 52,265)( 53,267)( 54,266)( 55,298)( 56,300)
( 57,299)( 58,304)( 59,306)( 60,305)( 61,301)( 62,303)( 63,302)( 64,307)
( 65,309)( 66,308)( 67,313)( 68,315)( 69,314)( 70,310)( 71,312)( 72,311)
( 73,316)( 74,318)( 75,317)( 76,322)( 77,324)( 78,323)( 79,319)( 80,321)
( 81,320)( 82,271)( 83,273)( 84,272)( 85,277)( 86,279)( 87,278)( 88,274)
( 89,276)( 90,275)( 91,280)( 92,282)( 93,281)( 94,286)( 95,288)( 96,287)
( 97,283)( 98,285)( 99,284)(100,289)(101,291)(102,290)(103,295)(104,297)
(105,296)(106,292)(107,294)(108,293)(109,379)(110,381)(111,380)(112,385)
(113,387)(114,386)(115,382)(116,384)(117,383)(118,388)(119,390)(120,389)
(121,394)(122,396)(123,395)(124,391)(125,393)(126,392)(127,397)(128,399)
(129,398)(130,403)(131,405)(132,404)(133,400)(134,402)(135,401)(136,406)
(137,408)(138,407)(139,412)(140,414)(141,413)(142,409)(143,411)(144,410)
(145,415)(146,417)(147,416)(148,421)(149,423)(150,422)(151,418)(152,420)
(153,419)(154,424)(155,426)(156,425)(157,430)(158,432)(159,431)(160,427)
(161,429)(162,428)(163,325)(164,327)(165,326)(166,331)(167,333)(168,332)
(169,328)(170,330)(171,329)(172,334)(173,336)(174,335)(175,340)(176,342)
(177,341)(178,337)(179,339)(180,338)(181,343)(182,345)(183,344)(184,349)
(185,351)(186,350)(187,346)(188,348)(189,347)(190,352)(191,354)(192,353)
(193,358)(194,360)(195,359)(196,355)(197,357)(198,356)(199,361)(200,363)
(201,362)(202,367)(203,369)(204,368)(205,364)(206,366)(207,365)(208,370)
(209,372)(210,371)(211,376)(212,378)(213,377)(214,373)(215,375)(216,374);;
s3 := (  1,  2)(  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)
( 25, 26)( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 40, 41)( 43, 44)( 46, 47)
( 49, 50)( 52, 53)( 55, 83)( 56, 82)( 57, 84)( 58, 86)( 59, 85)( 60, 87)
( 61, 89)( 62, 88)( 63, 90)( 64, 92)( 65, 91)( 66, 93)( 67, 95)( 68, 94)
( 69, 96)( 70, 98)( 71, 97)( 72, 99)( 73,101)( 74,100)( 75,102)( 76,104)
( 77,103)( 78,105)( 79,107)( 80,106)( 81,108)(109,164)(110,163)(111,165)
(112,167)(113,166)(114,168)(115,170)(116,169)(117,171)(118,173)(119,172)
(120,174)(121,176)(122,175)(123,177)(124,179)(125,178)(126,180)(127,182)
(128,181)(129,183)(130,185)(131,184)(132,186)(133,188)(134,187)(135,189)
(136,191)(137,190)(138,192)(139,194)(140,193)(141,195)(142,197)(143,196)
(144,198)(145,200)(146,199)(147,201)(148,203)(149,202)(150,204)(151,206)
(152,205)(153,207)(154,209)(155,208)(156,210)(157,212)(158,211)(159,213)
(160,215)(161,214)(162,216)(217,272)(218,271)(219,273)(220,275)(221,274)
(222,276)(223,278)(224,277)(225,279)(226,281)(227,280)(228,282)(229,284)
(230,283)(231,285)(232,287)(233,286)(234,288)(235,290)(236,289)(237,291)
(238,293)(239,292)(240,294)(241,296)(242,295)(243,297)(244,299)(245,298)
(246,300)(247,302)(248,301)(249,303)(250,305)(251,304)(252,306)(253,308)
(254,307)(255,309)(256,311)(257,310)(258,312)(259,314)(260,313)(261,315)
(262,317)(263,316)(264,318)(265,320)(266,319)(267,321)(268,323)(269,322)
(270,324)(325,353)(326,352)(327,354)(328,356)(329,355)(330,357)(331,359)
(332,358)(333,360)(334,362)(335,361)(336,363)(337,365)(338,364)(339,366)
(340,368)(341,367)(342,369)(343,371)(344,370)(345,372)(346,374)(347,373)
(348,375)(349,377)(350,376)(351,378)(379,380)(382,383)(385,386)(388,389)
(391,392)(394,395)(397,398)(400,401)(403,404)(406,407)(409,410)(412,413)
(415,416)(418,419)(421,422)(424,425)(427,428)(430,431);;
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,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

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

```
References : None.
to this polytope