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# Polytope of Type {24,8}

Atlas Canonical Name : {24,8}*768h
if this polytope has a name.
Group : SmallGroup(768,90329)
Rank : 3
Schlafli Type : {24,8}
Number of vertices, edges, etc : 48, 192, 16
Order of s0s1s2 : 24
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie
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}*256g
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, 30)( 26, 29)( 27, 28)( 31, 36)( 32, 35)( 33, 34)
( 37, 48)( 38, 47)( 39, 46)( 40, 45)( 41, 44)( 42, 43)( 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, 75)( 76, 78)( 79, 81)( 82, 84)( 85, 93)( 86, 92)
( 87, 91)( 88, 96)( 89, 95)( 90, 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)
(109,141)(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)(217,270)(218,269)(219,268)(220,267)
(221,266)(222,265)(223,276)(224,275)(225,274)(226,273)(227,272)(228,271)
(229,288)(230,287)(231,286)(232,285)(233,284)(234,283)(235,282)(236,281)
(237,280)(238,279)(239,278)(240,277)(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)
( 25,331)( 26,332)( 27,333)( 28,334)( 29,335)( 30,336)( 31,325)( 32,326)
( 33,327)( 34,328)( 35,329)( 36,330)( 37,319)( 38,320)( 39,321)( 40,322)
( 41,323)( 42,324)( 43,313)( 44,314)( 45,315)( 46,316)( 47,317)( 48,318)
( 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)
( 73,370)( 74,371)( 75,372)( 76,367)( 77,368)( 78,369)( 79,364)( 80,365)
( 81,366)( 82,361)( 83,362)( 84,363)( 85,379)( 86,380)( 87,381)( 88,382)
( 89,383)( 90,384)( 91,373)( 92,374)( 93,375)( 94,376)( 95,377)( 96,378)
( 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)
(121,235)(122,236)(123,237)(124,238)(125,239)(126,240)(127,229)(128,230)
(129,231)(130,232)(131,233)(132,234)(133,223)(134,224)(135,225)(136,226)
(137,227)(138,228)(139,217)(140,218)(141,219)(142,220)(143,221)(144,222)
(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)
(169,274)(170,275)(171,276)(172,271)(173,272)(174,273)(175,268)(176,269)
(177,270)(178,265)(179,266)(180,267)(181,283)(182,284)(183,285)(184,286)
(185,287)(186,288)(187,277)(188,278)(189,279)(190,280)(191,281)(192,282);;
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*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*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, 30)( 26, 29)( 27, 28)( 31, 36)( 32, 35)
( 33, 34)( 37, 48)( 38, 47)( 39, 46)( 40, 45)( 41, 44)( 42, 43)( 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, 75)( 76, 78)( 79, 81)( 82, 84)( 85, 93)
( 86, 92)( 87, 91)( 88, 96)( 89, 95)( 90, 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)(109,141)(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)(217,270)(218,269)(219,268)
(220,267)(221,266)(222,265)(223,276)(224,275)(225,274)(226,273)(227,272)
(228,271)(229,288)(230,287)(231,286)(232,285)(233,284)(234,283)(235,282)
(236,281)(237,280)(238,279)(239,278)(240,277)(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)( 25,331)( 26,332)( 27,333)( 28,334)( 29,335)( 30,336)( 31,325)
( 32,326)( 33,327)( 34,328)( 35,329)( 36,330)( 37,319)( 38,320)( 39,321)
( 40,322)( 41,323)( 42,324)( 43,313)( 44,314)( 45,315)( 46,316)( 47,317)
( 48,318)( 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)( 73,370)( 74,371)( 75,372)( 76,367)( 77,368)( 78,369)( 79,364)
( 80,365)( 81,366)( 82,361)( 83,362)( 84,363)( 85,379)( 86,380)( 87,381)
( 88,382)( 89,383)( 90,384)( 91,373)( 92,374)( 93,375)( 94,376)( 95,377)
( 96,378)( 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)(121,235)(122,236)(123,237)(124,238)(125,239)(126,240)(127,229)
(128,230)(129,231)(130,232)(131,233)(132,234)(133,223)(134,224)(135,225)
(136,226)(137,227)(138,228)(139,217)(140,218)(141,219)(142,220)(143,221)
(144,222)(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)(169,274)(170,275)(171,276)(172,271)(173,272)(174,273)(175,268)
(176,269)(177,270)(178,265)(179,266)(180,267)(181,283)(182,284)(183,285)
(184,286)(185,287)(186,288)(187,277)(188,278)(189,279)(190,280)(191,281)
(192,282);
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*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```
References : None.
to this polytope