Polytope of Type {6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12}*1152d
if this polytope has a name.
Group : SmallGroup(1152,155849)
Rank : 3
Schlafli Type : {6,12}
Number of vertices, edges, etc : 48, 288, 96
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 8
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}*576b
   3-fold quotients : {6,4}*384b
   4-fold quotients : {6,12}*288a
   6-fold quotients : {6,4}*192b
   8-fold quotients : {6,12}*144a, {6,12}*144d
   12-fold quotients : {6,4}*96
   16-fold quotients : {6,6}*72a
   24-fold quotients : {2,12}*48, {6,4}*48a, {3,4}*48, {6,4}*48b, {6,4}*48c
   48-fold quotients : {3,4}*24, {2,6}*24, {6,2}*24
   72-fold quotients : {2,4}*16
   96-fold quotients : {2,3}*12, {3,2}*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, 98)( 74, 97)( 75,104)( 76,103)( 77,101)
( 78,102)( 79,100)( 80, 99)( 81,114)( 82,113)( 83,120)( 84,119)( 85,117)
( 86,118)( 87,116)( 88,115)( 89,106)( 90,105)( 91,112)( 92,111)( 93,109)
( 94,110)( 95,108)( 96,107)(121,122)(123,128)(124,127)(129,138)(130,137)
(131,144)(132,143)(133,141)(134,142)(135,140)(136,139)(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)(  3,154)(  4,153)(  5,159)(  6,160)(  7,158)(  8,157)
(  9,147)( 10,148)( 11,146)( 12,145)( 13,151)( 14,152)( 15,150)( 16,149)
( 17,163)( 18,164)( 19,162)( 20,161)( 21,167)( 22,168)( 23,166)( 24,165)
( 25,179)( 26,180)( 27,178)( 28,177)( 29,183)( 30,184)( 31,182)( 32,181)
( 33,171)( 34,172)( 35,170)( 36,169)( 37,175)( 38,176)( 39,174)( 40,173)
( 41,187)( 42,188)( 43,186)( 44,185)( 45,191)( 46,192)( 47,190)( 48,189)
( 49,203)( 50,204)( 51,202)( 52,201)( 53,207)( 54,208)( 55,206)( 56,205)
( 57,195)( 58,196)( 59,194)( 60,193)( 61,199)( 62,200)( 63,198)( 64,197)
( 65,211)( 66,212)( 67,210)( 68,209)( 69,215)( 70,216)( 71,214)( 72,213)
( 73,228)( 74,227)( 75,225)( 76,226)( 77,232)( 78,231)( 79,229)( 80,230)
( 81,220)( 82,219)( 83,217)( 84,218)( 85,224)( 86,223)( 87,221)( 88,222)
( 89,236)( 90,235)( 91,233)( 92,234)( 93,240)( 94,239)( 95,237)( 96,238)
( 97,252)( 98,251)( 99,249)(100,250)(101,256)(102,255)(103,253)(104,254)
(105,244)(106,243)(107,241)(108,242)(109,248)(110,247)(111,245)(112,246)
(113,260)(114,259)(115,257)(116,258)(117,264)(118,263)(119,261)(120,262)
(121,276)(122,275)(123,273)(124,274)(125,280)(126,279)(127,277)(128,278)
(129,268)(130,267)(131,265)(132,266)(133,272)(134,271)(135,269)(136,270)
(137,284)(138,283)(139,281)(140,282)(141,288)(142,287)(143,285)(144,286);;
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, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s1*s0*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*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, 98)( 74, 97)( 75,104)( 76,103)
( 77,101)( 78,102)( 79,100)( 80, 99)( 81,114)( 82,113)( 83,120)( 84,119)
( 85,117)( 86,118)( 87,116)( 88,115)( 89,106)( 90,105)( 91,112)( 92,111)
( 93,109)( 94,110)( 95,108)( 96,107)(121,122)(123,128)(124,127)(129,138)
(130,137)(131,144)(132,143)(133,141)(134,142)(135,140)(136,139)(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)(  3,154)(  4,153)(  5,159)(  6,160)(  7,158)
(  8,157)(  9,147)( 10,148)( 11,146)( 12,145)( 13,151)( 14,152)( 15,150)
( 16,149)( 17,163)( 18,164)( 19,162)( 20,161)( 21,167)( 22,168)( 23,166)
( 24,165)( 25,179)( 26,180)( 27,178)( 28,177)( 29,183)( 30,184)( 31,182)
( 32,181)( 33,171)( 34,172)( 35,170)( 36,169)( 37,175)( 38,176)( 39,174)
( 40,173)( 41,187)( 42,188)( 43,186)( 44,185)( 45,191)( 46,192)( 47,190)
( 48,189)( 49,203)( 50,204)( 51,202)( 52,201)( 53,207)( 54,208)( 55,206)
( 56,205)( 57,195)( 58,196)( 59,194)( 60,193)( 61,199)( 62,200)( 63,198)
( 64,197)( 65,211)( 66,212)( 67,210)( 68,209)( 69,215)( 70,216)( 71,214)
( 72,213)( 73,228)( 74,227)( 75,225)( 76,226)( 77,232)( 78,231)( 79,229)
( 80,230)( 81,220)( 82,219)( 83,217)( 84,218)( 85,224)( 86,223)( 87,221)
( 88,222)( 89,236)( 90,235)( 91,233)( 92,234)( 93,240)( 94,239)( 95,237)
( 96,238)( 97,252)( 98,251)( 99,249)(100,250)(101,256)(102,255)(103,253)
(104,254)(105,244)(106,243)(107,241)(108,242)(109,248)(110,247)(111,245)
(112,246)(113,260)(114,259)(115,257)(116,258)(117,264)(118,263)(119,261)
(120,262)(121,276)(122,275)(123,273)(124,274)(125,280)(126,279)(127,277)
(128,278)(129,268)(130,267)(131,265)(132,266)(133,272)(134,271)(135,269)
(136,270)(137,284)(138,283)(139,281)(140,282)(141,288)(142,287)(143,285)
(144,286);
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, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s1*s0*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*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope