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# Polytope of Type {16,24}

Atlas Canonical Name : {16,24}*768d
Also Known As : {16,24|2}. if this polytope has another name.
Group : SmallGroup(768,82995)
Rank : 3
Schlafli Type : {16,24}
Number of vertices, edges, etc : 16, 192, 24
Order of s0s1s2 : 48
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
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 : {8,24}*384b, {16,12}*384a
3-fold quotients : {16,8}*256d
4-fold quotients : {4,24}*192a, {8,12}*192a, {16,6}*192
6-fold quotients : {8,8}*128b, {16,4}*128a
8-fold quotients : {4,12}*96a, {2,24}*96, {8,6}*96
12-fold quotients : {4,8}*64a, {8,4}*64a, {16,2}*64
16-fold quotients : {2,12}*48, {4,6}*48a
24-fold quotients : {4,4}*32, {2,8}*32, {8,2}*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)
( 25,313)( 26,314)( 27,315)( 28,316)( 29,317)( 30,318)( 31,319)( 32,320)
( 33,321)( 34,322)( 35,323)( 36,324)( 37,328)( 38,329)( 39,330)( 40,325)
( 41,326)( 42,327)( 43,334)( 44,335)( 45,336)( 46,331)( 47,332)( 48,333)
( 49,355)( 50,356)( 51,357)( 52,358)( 53,359)( 54,360)( 55,349)( 56,350)
( 57,351)( 58,352)( 59,353)( 60,354)( 61,343)( 62,344)( 63,345)( 64,346)
( 65,347)( 66,348)( 67,337)( 68,338)( 69,339)( 70,340)( 71,341)( 72,342)
( 73,379)( 74,380)( 75,381)( 76,382)( 77,383)( 78,384)( 79,373)( 80,374)
( 81,375)( 82,376)( 83,377)( 84,378)( 85,367)( 86,368)( 87,369)( 88,370)
( 89,371)( 90,372)( 91,361)( 92,362)( 93,363)( 94,364)( 95,365)( 96,366)
( 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)
(121,217)(122,218)(123,219)(124,220)(125,221)(126,222)(127,223)(128,224)
(129,225)(130,226)(131,227)(132,228)(133,232)(134,233)(135,234)(136,229)
(137,230)(138,231)(139,238)(140,239)(141,240)(142,235)(143,236)(144,237)
(145,259)(146,260)(147,261)(148,262)(149,263)(150,264)(151,253)(152,254)
(153,255)(154,256)(155,257)(156,258)(157,247)(158,248)(159,249)(160,250)
(161,251)(162,252)(163,241)(164,242)(165,243)(166,244)(167,245)(168,246)
(169,283)(170,284)(171,285)(172,286)(173,287)(174,288)(175,277)(176,278)
(177,279)(178,280)(179,281)(180,282)(181,271)(182,272)(183,273)(184,274)
(185,275)(186,276)(187,265)(188,266)(189,267)(190,268)(191,269)(192,270);;
s1 := (  2,  3)(  5,  6)(  8,  9)( 11, 12)( 13, 16)( 14, 18)( 15, 17)( 19, 22)
( 20, 24)( 21, 23)( 25, 31)( 26, 33)( 27, 32)( 28, 34)( 29, 36)( 30, 35)
( 37, 46)( 38, 48)( 39, 47)( 40, 43)( 41, 45)( 42, 44)( 49, 61)( 50, 63)
( 51, 62)( 52, 64)( 53, 66)( 54, 65)( 55, 67)( 56, 69)( 57, 68)( 58, 70)
( 59, 72)( 60, 71)( 73, 91)( 74, 93)( 75, 92)( 76, 94)( 77, 96)( 78, 95)
( 79, 85)( 80, 87)( 81, 86)( 82, 88)( 83, 90)( 84, 89)( 97,121)( 98,123)
( 99,122)(100,124)(101,126)(102,125)(103,127)(104,129)(105,128)(106,130)
(107,132)(108,131)(109,136)(110,138)(111,137)(112,133)(113,135)(114,134)
(115,142)(116,144)(117,143)(118,139)(119,141)(120,140)(145,181)(146,183)
(147,182)(148,184)(149,186)(150,185)(151,187)(152,189)(153,188)(154,190)
(155,192)(156,191)(157,169)(158,171)(159,170)(160,172)(161,174)(162,173)
(163,175)(164,177)(165,176)(166,178)(167,180)(168,179)(193,241)(194,243)
(195,242)(196,244)(197,246)(198,245)(199,247)(200,249)(201,248)(202,250)
(203,252)(204,251)(205,256)(206,258)(207,257)(208,253)(209,255)(210,254)
(211,262)(212,264)(213,263)(214,259)(215,261)(216,260)(217,271)(218,273)
(219,272)(220,274)(221,276)(222,275)(223,265)(224,267)(225,266)(226,268)
(227,270)(228,269)(229,286)(230,288)(231,287)(232,283)(233,285)(234,284)
(235,280)(236,282)(237,281)(238,277)(239,279)(240,278)(289,367)(290,369)
(291,368)(292,370)(293,372)(294,371)(295,361)(296,363)(297,362)(298,364)
(299,366)(300,365)(301,382)(302,384)(303,383)(304,379)(305,381)(306,380)
(307,376)(308,378)(309,377)(310,373)(311,375)(312,374)(313,343)(314,345)
(315,344)(316,346)(317,348)(318,347)(319,337)(320,339)(321,338)(322,340)
(323,342)(324,341)(325,358)(326,360)(327,359)(328,355)(329,357)(330,356)
(331,352)(332,354)(333,353)(334,349)(335,351)(336,350);;
s2 := (  1, 99)(  2, 98)(  3, 97)(  4,102)(  5,101)(  6,100)(  7,105)(  8,104)
(  9,103)( 10,108)( 11,107)( 12,106)( 13,111)( 14,110)( 15,109)( 16,114)
( 17,113)( 18,112)( 19,117)( 20,116)( 21,115)( 22,120)( 23,119)( 24,118)
( 25,129)( 26,128)( 27,127)( 28,132)( 29,131)( 30,130)( 31,123)( 32,122)
( 33,121)( 34,126)( 35,125)( 36,124)( 37,141)( 38,140)( 39,139)( 40,144)
( 41,143)( 42,142)( 43,135)( 44,134)( 45,133)( 46,138)( 47,137)( 48,136)
( 49,153)( 50,152)( 51,151)( 52,156)( 53,155)( 54,154)( 55,147)( 56,146)
( 57,145)( 58,150)( 59,149)( 60,148)( 61,165)( 62,164)( 63,163)( 64,168)
( 65,167)( 66,166)( 67,159)( 68,158)( 69,157)( 70,162)( 71,161)( 72,160)
( 73,171)( 74,170)( 75,169)( 76,174)( 77,173)( 78,172)( 79,177)( 80,176)
( 81,175)( 82,180)( 83,179)( 84,178)( 85,183)( 86,182)( 87,181)( 88,186)
( 89,185)( 90,184)( 91,189)( 92,188)( 93,187)( 94,192)( 95,191)( 96,190)
(193,291)(194,290)(195,289)(196,294)(197,293)(198,292)(199,297)(200,296)
(201,295)(202,300)(203,299)(204,298)(205,303)(206,302)(207,301)(208,306)
(209,305)(210,304)(211,309)(212,308)(213,307)(214,312)(215,311)(216,310)
(217,321)(218,320)(219,319)(220,324)(221,323)(222,322)(223,315)(224,314)
(225,313)(226,318)(227,317)(228,316)(229,333)(230,332)(231,331)(232,336)
(233,335)(234,334)(235,327)(236,326)(237,325)(238,330)(239,329)(240,328)
(241,345)(242,344)(243,343)(244,348)(245,347)(246,346)(247,339)(248,338)
(249,337)(250,342)(251,341)(252,340)(253,357)(254,356)(255,355)(256,360)
(257,359)(258,358)(259,351)(260,350)(261,349)(262,354)(263,353)(264,352)
(265,363)(266,362)(267,361)(268,366)(269,365)(270,364)(271,369)(272,368)
(273,367)(274,372)(275,371)(276,370)(277,375)(278,374)(279,373)(280,378)
(281,377)(282,376)(283,381)(284,380)(285,379)(286,384)(287,383)(288,382);;
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*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
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)( 25,313)( 26,314)( 27,315)( 28,316)( 29,317)( 30,318)( 31,319)
( 32,320)( 33,321)( 34,322)( 35,323)( 36,324)( 37,328)( 38,329)( 39,330)
( 40,325)( 41,326)( 42,327)( 43,334)( 44,335)( 45,336)( 46,331)( 47,332)
( 48,333)( 49,355)( 50,356)( 51,357)( 52,358)( 53,359)( 54,360)( 55,349)
( 56,350)( 57,351)( 58,352)( 59,353)( 60,354)( 61,343)( 62,344)( 63,345)
( 64,346)( 65,347)( 66,348)( 67,337)( 68,338)( 69,339)( 70,340)( 71,341)
( 72,342)( 73,379)( 74,380)( 75,381)( 76,382)( 77,383)( 78,384)( 79,373)
( 80,374)( 81,375)( 82,376)( 83,377)( 84,378)( 85,367)( 86,368)( 87,369)
( 88,370)( 89,371)( 90,372)( 91,361)( 92,362)( 93,363)( 94,364)( 95,365)
( 96,366)( 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)(121,217)(122,218)(123,219)(124,220)(125,221)(126,222)(127,223)
(128,224)(129,225)(130,226)(131,227)(132,228)(133,232)(134,233)(135,234)
(136,229)(137,230)(138,231)(139,238)(140,239)(141,240)(142,235)(143,236)
(144,237)(145,259)(146,260)(147,261)(148,262)(149,263)(150,264)(151,253)
(152,254)(153,255)(154,256)(155,257)(156,258)(157,247)(158,248)(159,249)
(160,250)(161,251)(162,252)(163,241)(164,242)(165,243)(166,244)(167,245)
(168,246)(169,283)(170,284)(171,285)(172,286)(173,287)(174,288)(175,277)
(176,278)(177,279)(178,280)(179,281)(180,282)(181,271)(182,272)(183,273)
(184,274)(185,275)(186,276)(187,265)(188,266)(189,267)(190,268)(191,269)
(192,270);
s1 := Sym(384)!(  2,  3)(  5,  6)(  8,  9)( 11, 12)( 13, 16)( 14, 18)( 15, 17)
( 19, 22)( 20, 24)( 21, 23)( 25, 31)( 26, 33)( 27, 32)( 28, 34)( 29, 36)
( 30, 35)( 37, 46)( 38, 48)( 39, 47)( 40, 43)( 41, 45)( 42, 44)( 49, 61)
( 50, 63)( 51, 62)( 52, 64)( 53, 66)( 54, 65)( 55, 67)( 56, 69)( 57, 68)
( 58, 70)( 59, 72)( 60, 71)( 73, 91)( 74, 93)( 75, 92)( 76, 94)( 77, 96)
( 78, 95)( 79, 85)( 80, 87)( 81, 86)( 82, 88)( 83, 90)( 84, 89)( 97,121)
( 98,123)( 99,122)(100,124)(101,126)(102,125)(103,127)(104,129)(105,128)
(106,130)(107,132)(108,131)(109,136)(110,138)(111,137)(112,133)(113,135)
(114,134)(115,142)(116,144)(117,143)(118,139)(119,141)(120,140)(145,181)
(146,183)(147,182)(148,184)(149,186)(150,185)(151,187)(152,189)(153,188)
(154,190)(155,192)(156,191)(157,169)(158,171)(159,170)(160,172)(161,174)
(162,173)(163,175)(164,177)(165,176)(166,178)(167,180)(168,179)(193,241)
(194,243)(195,242)(196,244)(197,246)(198,245)(199,247)(200,249)(201,248)
(202,250)(203,252)(204,251)(205,256)(206,258)(207,257)(208,253)(209,255)
(210,254)(211,262)(212,264)(213,263)(214,259)(215,261)(216,260)(217,271)
(218,273)(219,272)(220,274)(221,276)(222,275)(223,265)(224,267)(225,266)
(226,268)(227,270)(228,269)(229,286)(230,288)(231,287)(232,283)(233,285)
(234,284)(235,280)(236,282)(237,281)(238,277)(239,279)(240,278)(289,367)
(290,369)(291,368)(292,370)(293,372)(294,371)(295,361)(296,363)(297,362)
(298,364)(299,366)(300,365)(301,382)(302,384)(303,383)(304,379)(305,381)
(306,380)(307,376)(308,378)(309,377)(310,373)(311,375)(312,374)(313,343)
(314,345)(315,344)(316,346)(317,348)(318,347)(319,337)(320,339)(321,338)
(322,340)(323,342)(324,341)(325,358)(326,360)(327,359)(328,355)(329,357)
(330,356)(331,352)(332,354)(333,353)(334,349)(335,351)(336,350);
s2 := Sym(384)!(  1, 99)(  2, 98)(  3, 97)(  4,102)(  5,101)(  6,100)(  7,105)
(  8,104)(  9,103)( 10,108)( 11,107)( 12,106)( 13,111)( 14,110)( 15,109)
( 16,114)( 17,113)( 18,112)( 19,117)( 20,116)( 21,115)( 22,120)( 23,119)
( 24,118)( 25,129)( 26,128)( 27,127)( 28,132)( 29,131)( 30,130)( 31,123)
( 32,122)( 33,121)( 34,126)( 35,125)( 36,124)( 37,141)( 38,140)( 39,139)
( 40,144)( 41,143)( 42,142)( 43,135)( 44,134)( 45,133)( 46,138)( 47,137)
( 48,136)( 49,153)( 50,152)( 51,151)( 52,156)( 53,155)( 54,154)( 55,147)
( 56,146)( 57,145)( 58,150)( 59,149)( 60,148)( 61,165)( 62,164)( 63,163)
( 64,168)( 65,167)( 66,166)( 67,159)( 68,158)( 69,157)( 70,162)( 71,161)
( 72,160)( 73,171)( 74,170)( 75,169)( 76,174)( 77,173)( 78,172)( 79,177)
( 80,176)( 81,175)( 82,180)( 83,179)( 84,178)( 85,183)( 86,182)( 87,181)
( 88,186)( 89,185)( 90,184)( 91,189)( 92,188)( 93,187)( 94,192)( 95,191)
( 96,190)(193,291)(194,290)(195,289)(196,294)(197,293)(198,292)(199,297)
(200,296)(201,295)(202,300)(203,299)(204,298)(205,303)(206,302)(207,301)
(208,306)(209,305)(210,304)(211,309)(212,308)(213,307)(214,312)(215,311)
(216,310)(217,321)(218,320)(219,319)(220,324)(221,323)(222,322)(223,315)
(224,314)(225,313)(226,318)(227,317)(228,316)(229,333)(230,332)(231,331)
(232,336)(233,335)(234,334)(235,327)(236,326)(237,325)(238,330)(239,329)
(240,328)(241,345)(242,344)(243,343)(244,348)(245,347)(246,346)(247,339)
(248,338)(249,337)(250,342)(251,341)(252,340)(253,357)(254,356)(255,355)
(256,360)(257,359)(258,358)(259,351)(260,350)(261,349)(262,354)(263,353)
(264,352)(265,363)(266,362)(267,361)(268,366)(269,365)(270,364)(271,369)
(272,368)(273,367)(274,372)(275,371)(276,370)(277,375)(278,374)(279,373)
(280,378)(281,377)(282,376)(283,381)(284,380)(285,379)(286,384)(287,383)
(288,382);
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*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

```
References : None.
to this polytope