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# Polytope of Type {6,12}

Atlas Canonical Name : {6,12}*1152a
if this polytope has a name.
Group : SmallGroup(1152,155788)
Rank : 3
Schlafli Type : {6,12}
Number of vertices, edges, etc : 48, 288, 96
Order of s0s1s2 : 24
Order of s0s1s2s1 : 12
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 : {6,12}*576a, {6,6}*576a, {6,12}*576d
3-fold quotients : {6,12}*384
4-fold quotients : {6,6}*288a
6-fold quotients : {6,12}*192a, {6,12}*192b, {6,6}*192b
8-fold quotients : {6,12}*144b, {6,3}*144
12-fold quotients : {3,12}*96, {6,6}*96
16-fold quotients : {6,6}*72b
24-fold quotients : {2,12}*48, {3,6}*48, {6,3}*48
32-fold quotients : {6,3}*36
48-fold quotients : {3,3}*24, {2,6}*24
72-fold quotients : {2,4}*16
96-fold quotients : {2,3}*12
144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (  3,  4)(  5,  7)(  6,  8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)( 21, 23)
( 22, 24)( 25, 49)( 26, 50)( 27, 52)( 28, 51)( 29, 55)( 30, 56)( 31, 53)
( 32, 54)( 33, 57)( 34, 58)( 35, 60)( 36, 59)( 37, 63)( 38, 64)( 39, 61)
( 40, 62)( 41, 65)( 42, 66)( 43, 68)( 44, 67)( 45, 71)( 46, 72)( 47, 69)
( 48, 70)( 75, 76)( 77, 79)( 78, 80)( 83, 84)( 85, 87)( 86, 88)( 91, 92)
( 93, 95)( 94, 96)( 97,121)( 98,122)( 99,124)(100,123)(101,127)(102,128)
(103,125)(104,126)(105,129)(106,130)(107,132)(108,131)(109,135)(110,136)
(111,133)(112,134)(113,137)(114,138)(115,140)(116,139)(117,143)(118,144)
(119,141)(120,142)(145,146)(149,152)(150,151)(153,154)(157,160)(158,159)
(161,162)(165,168)(166,167)(169,194)(170,193)(171,195)(172,196)(173,200)
(174,199)(175,198)(176,197)(177,202)(178,201)(179,203)(180,204)(181,208)
(182,207)(183,206)(184,205)(185,210)(186,209)(187,211)(188,212)(189,216)
(190,215)(191,214)(192,213)(217,218)(221,224)(222,223)(225,226)(229,232)
(230,231)(233,234)(237,240)(238,239)(241,266)(242,265)(243,267)(244,268)
(245,272)(246,271)(247,270)(248,269)(249,274)(250,273)(251,275)(252,276)
(253,280)(254,279)(255,278)(256,277)(257,282)(258,281)(259,283)(260,284)
(261,288)(262,287)(263,286)(264,285);;
s1 := (  1, 25)(  2, 26)(  3, 31)(  4, 32)(  5, 30)(  6, 29)(  7, 27)(  8, 28)
(  9, 41)( 10, 42)( 11, 47)( 12, 48)( 13, 46)( 14, 45)( 15, 43)( 16, 44)
( 17, 33)( 18, 34)( 19, 39)( 20, 40)( 21, 38)( 22, 37)( 23, 35)( 24, 36)
( 51, 55)( 52, 56)( 53, 54)( 57, 65)( 58, 66)( 59, 71)( 60, 72)( 61, 70)
( 62, 69)( 63, 67)( 64, 68)( 73, 97)( 74, 98)( 75,103)( 76,104)( 77,102)
( 78,101)( 79, 99)( 80,100)( 81,113)( 82,114)( 83,119)( 84,120)( 85,118)
( 86,117)( 87,115)( 88,116)( 89,105)( 90,106)( 91,111)( 92,112)( 93,110)
( 94,109)( 95,107)( 96,108)(123,127)(124,128)(125,126)(129,137)(130,138)
(131,143)(132,144)(133,142)(134,141)(135,139)(136,140)(145,242)(146,241)
(147,248)(148,247)(149,245)(150,246)(151,244)(152,243)(153,258)(154,257)
(155,264)(156,263)(157,261)(158,262)(159,260)(160,259)(161,250)(162,249)
(163,256)(164,255)(165,253)(166,254)(167,252)(168,251)(169,218)(170,217)
(171,224)(172,223)(173,221)(174,222)(175,220)(176,219)(177,234)(178,233)
(179,240)(180,239)(181,237)(182,238)(183,236)(184,235)(185,226)(186,225)
(187,232)(188,231)(189,229)(190,230)(191,228)(192,227)(193,266)(194,265)
(195,272)(196,271)(197,269)(198,270)(199,268)(200,267)(201,282)(202,281)
(203,288)(204,287)(205,285)(206,286)(207,284)(208,283)(209,274)(210,273)
(211,280)(212,279)(213,277)(214,278)(215,276)(216,275);;
s2 := (  1,155)(  2,156)(  3,153)(  4,154)(  5,158)(  6,157)(  7,159)(  8,160)
(  9,147)( 10,148)( 11,145)( 12,146)( 13,150)( 14,149)( 15,151)( 16,152)
( 17,163)( 18,164)( 19,161)( 20,162)( 21,166)( 22,165)( 23,167)( 24,168)
( 25,203)( 26,204)( 27,201)( 28,202)( 29,206)( 30,205)( 31,207)( 32,208)
( 33,195)( 34,196)( 35,193)( 36,194)( 37,198)( 38,197)( 39,199)( 40,200)
( 41,211)( 42,212)( 43,209)( 44,210)( 45,214)( 46,213)( 47,215)( 48,216)
( 49,179)( 50,180)( 51,177)( 52,178)( 53,182)( 54,181)( 55,183)( 56,184)
( 57,171)( 58,172)( 59,169)( 60,170)( 61,174)( 62,173)( 63,175)( 64,176)
( 65,187)( 66,188)( 67,185)( 68,186)( 69,190)( 70,189)( 71,191)( 72,192)
( 73,227)( 74,228)( 75,225)( 76,226)( 77,230)( 78,229)( 79,231)( 80,232)
( 81,219)( 82,220)( 83,217)( 84,218)( 85,222)( 86,221)( 87,223)( 88,224)
( 89,235)( 90,236)( 91,233)( 92,234)( 93,238)( 94,237)( 95,239)( 96,240)
( 97,275)( 98,276)( 99,273)(100,274)(101,278)(102,277)(103,279)(104,280)
(105,267)(106,268)(107,265)(108,266)(109,270)(110,269)(111,271)(112,272)
(113,283)(114,284)(115,281)(116,282)(117,286)(118,285)(119,287)(120,288)
(121,251)(122,252)(123,249)(124,250)(125,254)(126,253)(127,255)(128,256)
(129,243)(130,244)(131,241)(132,242)(133,246)(134,245)(135,247)(136,248)
(137,259)(138,260)(139,257)(140,258)(141,262)(142,261)(143,263)(144,264);;
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*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*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*s2*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(288)!(  3,  4)(  5,  7)(  6,  8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)
( 21, 23)( 22, 24)( 25, 49)( 26, 50)( 27, 52)( 28, 51)( 29, 55)( 30, 56)
( 31, 53)( 32, 54)( 33, 57)( 34, 58)( 35, 60)( 36, 59)( 37, 63)( 38, 64)
( 39, 61)( 40, 62)( 41, 65)( 42, 66)( 43, 68)( 44, 67)( 45, 71)( 46, 72)
( 47, 69)( 48, 70)( 75, 76)( 77, 79)( 78, 80)( 83, 84)( 85, 87)( 86, 88)
( 91, 92)( 93, 95)( 94, 96)( 97,121)( 98,122)( 99,124)(100,123)(101,127)
(102,128)(103,125)(104,126)(105,129)(106,130)(107,132)(108,131)(109,135)
(110,136)(111,133)(112,134)(113,137)(114,138)(115,140)(116,139)(117,143)
(118,144)(119,141)(120,142)(145,146)(149,152)(150,151)(153,154)(157,160)
(158,159)(161,162)(165,168)(166,167)(169,194)(170,193)(171,195)(172,196)
(173,200)(174,199)(175,198)(176,197)(177,202)(178,201)(179,203)(180,204)
(181,208)(182,207)(183,206)(184,205)(185,210)(186,209)(187,211)(188,212)
(189,216)(190,215)(191,214)(192,213)(217,218)(221,224)(222,223)(225,226)
(229,232)(230,231)(233,234)(237,240)(238,239)(241,266)(242,265)(243,267)
(244,268)(245,272)(246,271)(247,270)(248,269)(249,274)(250,273)(251,275)
(252,276)(253,280)(254,279)(255,278)(256,277)(257,282)(258,281)(259,283)
(260,284)(261,288)(262,287)(263,286)(264,285);
s1 := Sym(288)!(  1, 25)(  2, 26)(  3, 31)(  4, 32)(  5, 30)(  6, 29)(  7, 27)
(  8, 28)(  9, 41)( 10, 42)( 11, 47)( 12, 48)( 13, 46)( 14, 45)( 15, 43)
( 16, 44)( 17, 33)( 18, 34)( 19, 39)( 20, 40)( 21, 38)( 22, 37)( 23, 35)
( 24, 36)( 51, 55)( 52, 56)( 53, 54)( 57, 65)( 58, 66)( 59, 71)( 60, 72)
( 61, 70)( 62, 69)( 63, 67)( 64, 68)( 73, 97)( 74, 98)( 75,103)( 76,104)
( 77,102)( 78,101)( 79, 99)( 80,100)( 81,113)( 82,114)( 83,119)( 84,120)
( 85,118)( 86,117)( 87,115)( 88,116)( 89,105)( 90,106)( 91,111)( 92,112)
( 93,110)( 94,109)( 95,107)( 96,108)(123,127)(124,128)(125,126)(129,137)
(130,138)(131,143)(132,144)(133,142)(134,141)(135,139)(136,140)(145,242)
(146,241)(147,248)(148,247)(149,245)(150,246)(151,244)(152,243)(153,258)
(154,257)(155,264)(156,263)(157,261)(158,262)(159,260)(160,259)(161,250)
(162,249)(163,256)(164,255)(165,253)(166,254)(167,252)(168,251)(169,218)
(170,217)(171,224)(172,223)(173,221)(174,222)(175,220)(176,219)(177,234)
(178,233)(179,240)(180,239)(181,237)(182,238)(183,236)(184,235)(185,226)
(186,225)(187,232)(188,231)(189,229)(190,230)(191,228)(192,227)(193,266)
(194,265)(195,272)(196,271)(197,269)(198,270)(199,268)(200,267)(201,282)
(202,281)(203,288)(204,287)(205,285)(206,286)(207,284)(208,283)(209,274)
(210,273)(211,280)(212,279)(213,277)(214,278)(215,276)(216,275);
s2 := Sym(288)!(  1,155)(  2,156)(  3,153)(  4,154)(  5,158)(  6,157)(  7,159)
(  8,160)(  9,147)( 10,148)( 11,145)( 12,146)( 13,150)( 14,149)( 15,151)
( 16,152)( 17,163)( 18,164)( 19,161)( 20,162)( 21,166)( 22,165)( 23,167)
( 24,168)( 25,203)( 26,204)( 27,201)( 28,202)( 29,206)( 30,205)( 31,207)
( 32,208)( 33,195)( 34,196)( 35,193)( 36,194)( 37,198)( 38,197)( 39,199)
( 40,200)( 41,211)( 42,212)( 43,209)( 44,210)( 45,214)( 46,213)( 47,215)
( 48,216)( 49,179)( 50,180)( 51,177)( 52,178)( 53,182)( 54,181)( 55,183)
( 56,184)( 57,171)( 58,172)( 59,169)( 60,170)( 61,174)( 62,173)( 63,175)
( 64,176)( 65,187)( 66,188)( 67,185)( 68,186)( 69,190)( 70,189)( 71,191)
( 72,192)( 73,227)( 74,228)( 75,225)( 76,226)( 77,230)( 78,229)( 79,231)
( 80,232)( 81,219)( 82,220)( 83,217)( 84,218)( 85,222)( 86,221)( 87,223)
( 88,224)( 89,235)( 90,236)( 91,233)( 92,234)( 93,238)( 94,237)( 95,239)
( 96,240)( 97,275)( 98,276)( 99,273)(100,274)(101,278)(102,277)(103,279)
(104,280)(105,267)(106,268)(107,265)(108,266)(109,270)(110,269)(111,271)
(112,272)(113,283)(114,284)(115,281)(116,282)(117,286)(118,285)(119,287)
(120,288)(121,251)(122,252)(123,249)(124,250)(125,254)(126,253)(127,255)
(128,256)(129,243)(130,244)(131,241)(132,242)(133,246)(134,245)(135,247)
(136,248)(137,259)(138,260)(139,257)(140,258)(141,262)(142,261)(143,263)
(144,264);
poly := sub<Sym(288)|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*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*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*s2*s1*s2 >;

```
References : None.
to this polytope