Questions?
See the FAQ
or other info.

# Polytope of Type {12,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8}*768g
if this polytope has a name.
Group : SmallGroup(768,1086012)
Rank : 3
Schlafli Type : {12,8}
Number of vertices, edges, etc : 48, 192, 32
Order of s0s1s2 : 12
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-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 : {12,4}*384c, {6,8}*384b
4-fold quotients : {6,4}*192a
8-fold quotients : {12,4}*96c
16-fold quotients : {6,4}*48c
32-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (  5,  7)(  6,  8)( 13, 15)( 14, 16)( 17, 25)( 18, 26)( 19, 27)( 20, 28)
( 21, 31)( 22, 32)( 23, 29)( 24, 30)( 33, 65)( 34, 66)( 35, 67)( 36, 68)
( 37, 71)( 38, 72)( 39, 69)( 40, 70)( 41, 73)( 42, 74)( 43, 75)( 44, 76)
( 45, 79)( 46, 80)( 47, 77)( 48, 78)( 49, 89)( 50, 90)( 51, 91)( 52, 92)
( 53, 95)( 54, 96)( 55, 93)( 56, 94)( 57, 81)( 58, 82)( 59, 83)( 60, 84)
( 61, 87)( 62, 88)( 63, 85)( 64, 86)(101,103)(102,104)(109,111)(110,112)
(113,121)(114,122)(115,123)(116,124)(117,127)(118,128)(119,125)(120,126)
(129,161)(130,162)(131,163)(132,164)(133,167)(134,168)(135,165)(136,166)
(137,169)(138,170)(139,171)(140,172)(141,175)(142,176)(143,173)(144,174)
(145,185)(146,186)(147,187)(148,188)(149,191)(150,192)(151,189)(152,190)
(153,177)(154,178)(155,179)(156,180)(157,183)(158,184)(159,181)(160,182)
(193,289)(194,290)(195,291)(196,292)(197,295)(198,296)(199,293)(200,294)
(201,297)(202,298)(203,299)(204,300)(205,303)(206,304)(207,301)(208,302)
(209,313)(210,314)(211,315)(212,316)(213,319)(214,320)(215,317)(216,318)
(217,305)(218,306)(219,307)(220,308)(221,311)(222,312)(223,309)(224,310)
(225,353)(226,354)(227,355)(228,356)(229,359)(230,360)(231,357)(232,358)
(233,361)(234,362)(235,363)(236,364)(237,367)(238,368)(239,365)(240,366)
(241,377)(242,378)(243,379)(244,380)(245,383)(246,384)(247,381)(248,382)
(249,369)(250,370)(251,371)(252,372)(253,375)(254,376)(255,373)(256,374)
(257,321)(258,322)(259,323)(260,324)(261,327)(262,328)(263,325)(264,326)
(265,329)(266,330)(267,331)(268,332)(269,335)(270,336)(271,333)(272,334)
(273,345)(274,346)(275,347)(276,348)(277,351)(278,352)(279,349)(280,350)
(281,337)(282,338)(283,339)(284,340)(285,343)(286,344)(287,341)(288,342);;
s1 := (  1,353)(  2,354)(  3,357)(  4,358)(  5,355)(  6,356)(  7,359)(  8,360)
(  9,374)( 10,373)( 11,370)( 12,369)( 13,376)( 14,375)( 15,372)( 16,371)
( 17,364)( 18,363)( 19,368)( 20,367)( 21,362)( 22,361)( 23,366)( 24,365)
( 25,384)( 26,383)( 27,380)( 28,379)( 29,382)( 30,381)( 31,378)( 32,377)
( 33,321)( 34,322)( 35,325)( 36,326)( 37,323)( 38,324)( 39,327)( 40,328)
( 41,342)( 42,341)( 43,338)( 44,337)( 45,344)( 46,343)( 47,340)( 48,339)
( 49,332)( 50,331)( 51,336)( 52,335)( 53,330)( 54,329)( 55,334)( 56,333)
( 57,352)( 58,351)( 59,348)( 60,347)( 61,350)( 62,349)( 63,346)( 64,345)
( 65,289)( 66,290)( 67,293)( 68,294)( 69,291)( 70,292)( 71,295)( 72,296)
( 73,310)( 74,309)( 75,306)( 76,305)( 77,312)( 78,311)( 79,308)( 80,307)
( 81,300)( 82,299)( 83,304)( 84,303)( 85,298)( 86,297)( 87,302)( 88,301)
( 89,320)( 90,319)( 91,316)( 92,315)( 93,318)( 94,317)( 95,314)( 96,313)
( 97,257)( 98,258)( 99,261)(100,262)(101,259)(102,260)(103,263)(104,264)
(105,278)(106,277)(107,274)(108,273)(109,280)(110,279)(111,276)(112,275)
(113,268)(114,267)(115,272)(116,271)(117,266)(118,265)(119,270)(120,269)
(121,288)(122,287)(123,284)(124,283)(125,286)(126,285)(127,282)(128,281)
(129,225)(130,226)(131,229)(132,230)(133,227)(134,228)(135,231)(136,232)
(137,246)(138,245)(139,242)(140,241)(141,248)(142,247)(143,244)(144,243)
(145,236)(146,235)(147,240)(148,239)(149,234)(150,233)(151,238)(152,237)
(153,256)(154,255)(155,252)(156,251)(157,254)(158,253)(159,250)(160,249)
(161,193)(162,194)(163,197)(164,198)(165,195)(166,196)(167,199)(168,200)
(169,214)(170,213)(171,210)(172,209)(173,216)(174,215)(175,212)(176,211)
(177,204)(178,203)(179,208)(180,207)(181,202)(182,201)(183,206)(184,205)
(185,224)(186,223)(187,220)(188,219)(189,222)(190,221)(191,218)(192,217);;
s2 := (  1,105)(  2,106)(  3,107)(  4,108)(  5,110)(  6,109)(  7,112)(  8,111)
(  9, 97)( 10, 98)( 11, 99)( 12,100)( 13,102)( 14,101)( 15,104)( 16,103)
( 17,121)( 18,122)( 19,123)( 20,124)( 21,126)( 22,125)( 23,128)( 24,127)
( 25,113)( 26,114)( 27,115)( 28,116)( 29,118)( 30,117)( 31,120)( 32,119)
( 33,137)( 34,138)( 35,139)( 36,140)( 37,142)( 38,141)( 39,144)( 40,143)
( 41,129)( 42,130)( 43,131)( 44,132)( 45,134)( 46,133)( 47,136)( 48,135)
( 49,153)( 50,154)( 51,155)( 52,156)( 53,158)( 54,157)( 55,160)( 56,159)
( 57,145)( 58,146)( 59,147)( 60,148)( 61,150)( 62,149)( 63,152)( 64,151)
( 65,169)( 66,170)( 67,171)( 68,172)( 69,174)( 70,173)( 71,176)( 72,175)
( 73,161)( 74,162)( 75,163)( 76,164)( 77,166)( 78,165)( 79,168)( 80,167)
( 81,185)( 82,186)( 83,187)( 84,188)( 85,190)( 86,189)( 87,192)( 88,191)
( 89,177)( 90,178)( 91,179)( 92,180)( 93,182)( 94,181)( 95,184)( 96,183)
(193,297)(194,298)(195,299)(196,300)(197,302)(198,301)(199,304)(200,303)
(201,289)(202,290)(203,291)(204,292)(205,294)(206,293)(207,296)(208,295)
(209,313)(210,314)(211,315)(212,316)(213,318)(214,317)(215,320)(216,319)
(217,305)(218,306)(219,307)(220,308)(221,310)(222,309)(223,312)(224,311)
(225,329)(226,330)(227,331)(228,332)(229,334)(230,333)(231,336)(232,335)
(233,321)(234,322)(235,323)(236,324)(237,326)(238,325)(239,328)(240,327)
(241,345)(242,346)(243,347)(244,348)(245,350)(246,349)(247,352)(248,351)
(249,337)(250,338)(251,339)(252,340)(253,342)(254,341)(255,344)(256,343)
(257,361)(258,362)(259,363)(260,364)(261,366)(262,365)(263,368)(264,367)
(265,353)(266,354)(267,355)(268,356)(269,358)(270,357)(271,360)(272,359)
(273,377)(274,378)(275,379)(276,380)(277,382)(278,381)(279,384)(280,383)
(281,369)(282,370)(283,371)(284,372)(285,374)(286,373)(287,376)(288,375);;
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*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope