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# Polytope of Type {8,24}

Atlas Canonical Name : {8,24}*768h
if this polytope has a name.
Group : SmallGroup(768,90329)
Rank : 3
Schlafli Type : {8,24}
Number of vertices, edges, etc : 16, 192, 48
Order of s0s1s2 : 24
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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 : {8,12}*384b
3-fold quotients : {8,8}*256h
4-fold quotients : {4,12}*192a
6-fold quotients : {8,4}*128b
8-fold quotients : {4,12}*96a
12-fold quotients : {4,4}*64
16-fold quotients : {2,12}*48, {4,6}*48a
24-fold quotients : {4,4}*32
32-fold quotients : {2,6}*24
48-fold quotients : {2,4}*16, {4,2}*16
64-fold quotients : {2,3}*12
96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (  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);;
s1 := (  2,  3)(  5,  6)(  8,  9)( 11, 12)( 13, 19)( 14, 21)( 15, 20)( 16, 22)
( 17, 24)( 18, 23)( 25, 28)( 26, 30)( 27, 29)( 31, 34)( 32, 36)( 33, 35)
( 37, 46)( 38, 48)( 39, 47)( 40, 43)( 41, 45)( 42, 44)( 49, 52)( 50, 54)
( 51, 53)( 55, 58)( 56, 60)( 57, 59)( 61, 70)( 62, 72)( 63, 71)( 64, 67)
( 65, 69)( 66, 68)( 74, 75)( 77, 78)( 80, 81)( 83, 84)( 85, 91)( 86, 93)
( 87, 92)( 88, 94)( 89, 96)( 90, 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)
(109,139)(110,141)(111,140)(112,142)(113,144)(114,143)(115,133)(116,135)
(117,134)(118,136)(119,138)(120,137)(145,175)(146,177)(147,176)(148,178)
(149,180)(150,179)(151,169)(152,171)(153,170)(154,172)(155,174)(156,173)
(157,181)(158,183)(159,182)(160,184)(161,186)(162,185)(163,187)(164,189)
(165,188)(166,190)(167,192)(168,191)(193,241)(194,243)(195,242)(196,244)
(197,246)(198,245)(199,247)(200,249)(201,248)(202,250)(203,252)(204,251)
(205,259)(206,261)(207,260)(208,262)(209,264)(210,263)(211,253)(212,255)
(213,254)(214,256)(215,258)(216,257)(217,268)(218,270)(219,269)(220,265)
(221,267)(222,266)(223,274)(224,276)(225,275)(226,271)(227,273)(228,272)
(229,286)(230,288)(231,287)(232,283)(233,285)(234,284)(235,280)(236,282)
(237,281)(238,277)(239,279)(240,278)(289,376)(290,378)(291,377)(292,373)
(293,375)(294,374)(295,382)(296,384)(297,383)(298,379)(299,381)(300,380)
(301,367)(302,369)(303,368)(304,370)(305,372)(306,371)(307,361)(308,363)
(309,362)(310,364)(311,366)(312,365)(313,349)(314,351)(315,350)(316,352)
(317,354)(318,353)(319,355)(320,357)(321,356)(322,358)(323,360)(324,359)
(325,346)(326,348)(327,347)(328,343)(329,345)(330,344)(331,340)(332,342)
(333,341)(334,337)(335,339)(336,338);;
s2 := (  1,195)(  2,194)(  3,193)(  4,198)(  5,197)(  6,196)(  7,204)(  8,203)
(  9,202)( 10,201)( 11,200)( 12,199)( 13,207)( 14,206)( 15,205)( 16,210)
( 17,209)( 18,208)( 19,216)( 20,215)( 21,214)( 22,213)( 23,212)( 24,211)
( 25,240)( 26,239)( 27,238)( 28,237)( 29,236)( 30,235)( 31,231)( 32,230)
( 33,229)( 34,234)( 35,233)( 36,232)( 37,225)( 38,224)( 39,223)( 40,228)
( 41,227)( 42,226)( 43,222)( 44,221)( 45,220)( 46,219)( 47,218)( 48,217)
( 49,246)( 50,245)( 51,244)( 52,243)( 53,242)( 54,241)( 55,249)( 56,248)
( 57,247)( 58,252)( 59,251)( 60,250)( 61,258)( 62,257)( 63,256)( 64,255)
( 65,254)( 66,253)( 67,261)( 68,260)( 69,259)( 70,264)( 71,263)( 72,262)
( 73,285)( 74,284)( 75,283)( 76,288)( 77,287)( 78,286)( 79,282)( 80,281)
( 81,280)( 82,279)( 83,278)( 84,277)( 85,276)( 86,275)( 87,274)( 88,273)
( 89,272)( 90,271)( 91,267)( 92,266)( 93,265)( 94,270)( 95,269)( 96,268)
( 97,291)( 98,290)( 99,289)(100,294)(101,293)(102,292)(103,300)(104,299)
(105,298)(106,297)(107,296)(108,295)(109,303)(110,302)(111,301)(112,306)
(113,305)(114,304)(115,312)(116,311)(117,310)(118,309)(119,308)(120,307)
(121,336)(122,335)(123,334)(124,333)(125,332)(126,331)(127,327)(128,326)
(129,325)(130,330)(131,329)(132,328)(133,321)(134,320)(135,319)(136,324)
(137,323)(138,322)(139,318)(140,317)(141,316)(142,315)(143,314)(144,313)
(145,342)(146,341)(147,340)(148,339)(149,338)(150,337)(151,345)(152,344)
(153,343)(154,348)(155,347)(156,346)(157,354)(158,353)(159,352)(160,351)
(161,350)(162,349)(163,357)(164,356)(165,355)(166,360)(167,359)(168,358)
(169,381)(170,380)(171,379)(172,384)(173,383)(174,382)(175,378)(176,377)
(177,376)(178,375)(179,374)(180,373)(181,372)(182,371)(183,370)(184,369)
(185,368)(186,367)(187,363)(188,362)(189,361)(190,366)(191,365)(192,364);;
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, s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope