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# Polytope of Type {24,8}

Atlas Canonical Name : {24,8}*768f
if this polytope has a name.
Group : SmallGroup(768,90303)
Rank : 3
Schlafli Type : {24,8}
Number of vertices, edges, etc : 48, 192, 16
Order of s0s1s2 : 12
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {12,8}*384b
3-fold quotients : {8,8}*256e
4-fold quotients : {12,4}*192a
6-fold quotients : {4,8}*128b
8-fold quotients : {12,4}*96a
12-fold quotients : {4,4}*64
16-fold quotients : {12,2}*48, {6,4}*48a
24-fold quotients : {4,4}*32
32-fold quotients : {6,2}*24
48-fold quotients : {2,4}*16, {4,2}*16
64-fold quotients : {3,2}*12
96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (  1,193)(  2,195)(  3,194)(  4,196)(  5,198)(  6,197)(  7,202)(  8,204)
(  9,203)( 10,199)( 11,201)( 12,200)( 13,205)( 14,207)( 15,206)( 16,208)
( 17,210)( 18,209)( 19,214)( 20,216)( 21,215)( 22,211)( 23,213)( 24,212)
( 25,238)( 26,240)( 27,239)( 28,235)( 29,237)( 30,236)( 31,229)( 32,231)
( 33,230)( 34,232)( 35,234)( 36,233)( 37,223)( 38,225)( 39,224)( 40,226)
( 41,228)( 42,227)( 43,220)( 44,222)( 45,221)( 46,217)( 47,219)( 48,218)
( 49,244)( 50,246)( 51,245)( 52,241)( 53,243)( 54,242)( 55,247)( 56,249)
( 57,248)( 58,250)( 59,252)( 60,251)( 61,256)( 62,258)( 63,257)( 64,253)
( 65,255)( 66,254)( 67,259)( 68,261)( 69,260)( 70,262)( 71,264)( 72,263)
( 73,283)( 74,285)( 75,284)( 76,286)( 77,288)( 78,287)( 79,280)( 80,282)
( 81,281)( 82,277)( 83,279)( 84,278)( 85,274)( 86,276)( 87,275)( 88,271)
( 89,273)( 90,272)( 91,265)( 92,267)( 93,266)( 94,268)( 95,270)( 96,269)
( 97,289)( 98,291)( 99,290)(100,292)(101,294)(102,293)(103,298)(104,300)
(105,299)(106,295)(107,297)(108,296)(109,301)(110,303)(111,302)(112,304)
(113,306)(114,305)(115,310)(116,312)(117,311)(118,307)(119,309)(120,308)
(121,334)(122,336)(123,335)(124,331)(125,333)(126,332)(127,325)(128,327)
(129,326)(130,328)(131,330)(132,329)(133,319)(134,321)(135,320)(136,322)
(137,324)(138,323)(139,316)(140,318)(141,317)(142,313)(143,315)(144,314)
(145,340)(146,342)(147,341)(148,337)(149,339)(150,338)(151,343)(152,345)
(153,344)(154,346)(155,348)(156,347)(157,352)(158,354)(159,353)(160,349)
(161,351)(162,350)(163,355)(164,357)(165,356)(166,358)(167,360)(168,359)
(169,379)(170,381)(171,380)(172,382)(173,384)(174,383)(175,376)(176,378)
(177,377)(178,373)(179,375)(180,374)(181,370)(182,372)(183,371)(184,367)
(185,369)(186,368)(187,361)(188,363)(189,362)(190,364)(191,366)(192,365);;
s1 := (  1,  3)(  4,  6)(  7,  9)( 10, 12)( 13, 21)( 14, 20)( 15, 19)( 16, 24)
( 17, 23)( 18, 22)( 25, 27)( 28, 30)( 31, 33)( 34, 36)( 37, 45)( 38, 44)
( 39, 43)( 40, 48)( 41, 47)( 42, 46)( 49, 54)( 50, 53)( 51, 52)( 55, 60)
( 56, 59)( 57, 58)( 61, 72)( 62, 71)( 63, 70)( 64, 69)( 65, 68)( 66, 67)
( 73, 78)( 74, 77)( 75, 76)( 79, 84)( 80, 83)( 81, 82)( 85, 96)( 86, 95)
( 87, 94)( 88, 93)( 89, 92)( 90, 91)( 97,123)( 98,122)( 99,121)(100,126)
(101,125)(102,124)(103,129)(104,128)(105,127)(106,132)(107,131)(108,130)
(109,141)(110,140)(111,139)(112,144)(113,143)(114,142)(115,135)(116,134)
(117,133)(118,138)(119,137)(120,136)(145,177)(146,176)(147,175)(148,180)
(149,179)(150,178)(151,171)(152,170)(153,169)(154,174)(155,173)(156,172)
(157,183)(158,182)(159,181)(160,186)(161,185)(162,184)(163,189)(164,188)
(165,187)(166,192)(167,191)(168,190)(193,243)(194,242)(195,241)(196,246)
(197,245)(198,244)(199,249)(200,248)(201,247)(202,252)(203,251)(204,250)
(205,261)(206,260)(207,259)(208,264)(209,263)(210,262)(211,255)(212,254)
(213,253)(214,258)(215,257)(216,256)(217,267)(218,266)(219,265)(220,270)
(221,269)(222,268)(223,273)(224,272)(225,271)(226,276)(227,275)(228,274)
(229,285)(230,284)(231,283)(232,288)(233,287)(234,286)(235,279)(236,278)
(237,277)(238,282)(239,281)(240,280)(289,378)(290,377)(291,376)(292,375)
(293,374)(294,373)(295,384)(296,383)(297,382)(298,381)(299,380)(300,379)
(301,369)(302,368)(303,367)(304,372)(305,371)(306,370)(307,363)(308,362)
(309,361)(310,366)(311,365)(312,364)(313,351)(314,350)(315,349)(316,354)
(317,353)(318,352)(319,357)(320,356)(321,355)(322,360)(323,359)(324,358)
(325,348)(326,347)(327,346)(328,345)(329,344)(330,343)(331,342)(332,341)
(333,340)(334,339)(335,338)(336,337);;
s2 := (  1,289)(  2,290)(  3,291)(  4,292)(  5,293)(  6,294)(  7,295)(  8,296)
(  9,297)( 10,298)( 11,299)( 12,300)( 13,304)( 14,305)( 15,306)( 16,301)
( 17,302)( 18,303)( 19,310)( 20,311)( 21,312)( 22,307)( 23,308)( 24,309)
( 25,334)( 26,335)( 27,336)( 28,331)( 29,332)( 30,333)( 31,328)( 32,329)
( 33,330)( 34,325)( 35,326)( 36,327)( 37,322)( 38,323)( 39,324)( 40,319)
( 41,320)( 42,321)( 43,316)( 44,317)( 45,318)( 46,313)( 47,314)( 48,315)
( 49,352)( 50,353)( 51,354)( 52,349)( 53,350)( 54,351)( 55,358)( 56,359)
( 57,360)( 58,355)( 59,356)( 60,357)( 61,340)( 62,341)( 63,342)( 64,337)
( 65,338)( 66,339)( 67,346)( 68,347)( 69,348)( 70,343)( 71,344)( 72,345)
( 73,367)( 74,368)( 75,369)( 76,370)( 77,371)( 78,372)( 79,361)( 80,362)
( 81,363)( 82,364)( 83,365)( 84,366)( 85,382)( 86,383)( 87,384)( 88,379)
( 89,380)( 90,381)( 91,376)( 92,377)( 93,378)( 94,373)( 95,374)( 96,375)
( 97,193)( 98,194)( 99,195)(100,196)(101,197)(102,198)(103,199)(104,200)
(105,201)(106,202)(107,203)(108,204)(109,208)(110,209)(111,210)(112,205)
(113,206)(114,207)(115,214)(116,215)(117,216)(118,211)(119,212)(120,213)
(121,238)(122,239)(123,240)(124,235)(125,236)(126,237)(127,232)(128,233)
(129,234)(130,229)(131,230)(132,231)(133,226)(134,227)(135,228)(136,223)
(137,224)(138,225)(139,220)(140,221)(141,222)(142,217)(143,218)(144,219)
(145,256)(146,257)(147,258)(148,253)(149,254)(150,255)(151,262)(152,263)
(153,264)(154,259)(155,260)(156,261)(157,244)(158,245)(159,246)(160,241)
(161,242)(162,243)(163,250)(164,251)(165,252)(166,247)(167,248)(168,249)
(169,271)(170,272)(171,273)(172,274)(173,275)(174,276)(175,265)(176,266)
(177,267)(178,268)(179,269)(180,270)(181,286)(182,287)(183,288)(184,283)
(185,284)(186,285)(187,280)(188,281)(189,282)(190,277)(191,278)(192,279);;
poly := Group([s0,s1,s2]);;

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

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

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

```
References : None.
to this polytope