Polytope of Type {52,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {52,6}*1872
if this polytope has a name.
Group : SmallGroup(1872,1058)
Rank : 3
Schlafli Type : {52,6}
Number of vertices, edges, etc : 156, 468, 18
Order of s₀s₁s₂ : 52
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {52,6}*936
   9-fold quotients : {52,2}*208
   13-fold quotients : {4,6}*144
   18-fold quotients : {26,2}*104
   26-fold quotients : {4,6}*72
   36-fold quotients : {13,2}*52
   117-fold quotients : {4,2}*16
   234-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 13)(  3, 12)(  4, 11)(  5, 10)(  6,  9)(  7,  8)( 15, 26)( 16, 25)
( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 28, 39)( 29, 38)( 30, 37)( 31, 36)
( 32, 35)( 33, 34)( 40, 79)( 41, 91)( 42, 90)( 43, 89)( 44, 88)( 45, 87)
( 46, 86)( 47, 85)( 48, 84)( 49, 83)( 50, 82)( 51, 81)( 52, 80)( 53, 92)
( 54,104)( 55,103)( 56,102)( 57,101)( 58,100)( 59, 99)( 60, 98)( 61, 97)
( 62, 96)( 63, 95)( 64, 94)( 65, 93)( 66,105)( 67,117)( 68,116)( 69,115)
( 70,114)( 71,113)( 72,112)( 73,111)( 74,110)( 75,109)( 76,108)( 77,107)
( 78,106)(119,130)(120,129)(121,128)(122,127)(123,126)(124,125)(132,143)
(133,142)(134,141)(135,140)(136,139)(137,138)(145,156)(146,155)(147,154)
(148,153)(149,152)(150,151)(157,196)(158,208)(159,207)(160,206)(161,205)
(162,204)(163,203)(164,202)(165,201)(166,200)(167,199)(168,198)(169,197)
(170,209)(171,221)(172,220)(173,219)(174,218)(175,217)(176,216)(177,215)
(178,214)(179,213)(180,212)(181,211)(182,210)(183,222)(184,234)(185,233)
(186,232)(187,231)(188,230)(189,229)(190,228)(191,227)(192,226)(193,225)
(194,224)(195,223);;
s1 := (  1,  2)(  3, 13)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 14, 80)( 15, 79)
( 16, 91)( 17, 90)( 18, 89)( 19, 88)( 20, 87)( 21, 86)( 22, 85)( 23, 84)
( 24, 83)( 25, 82)( 26, 81)( 27, 41)( 28, 40)( 29, 52)( 30, 51)( 31, 50)
( 32, 49)( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)( 38, 43)( 39, 42)
( 53,106)( 54,105)( 55,117)( 56,116)( 57,115)( 58,114)( 59,113)( 60,112)
( 61,111)( 62,110)( 63,109)( 64,108)( 65,107)( 66, 67)( 68, 78)( 69, 77)
( 70, 76)( 71, 75)( 72, 74)( 92, 93)( 94,104)( 95,103)( 96,102)( 97,101)
( 98,100)(118,119)(120,130)(121,129)(122,128)(123,127)(124,126)(131,197)
(132,196)(133,208)(134,207)(135,206)(136,205)(137,204)(138,203)(139,202)
(140,201)(141,200)(142,199)(143,198)(144,158)(145,157)(146,169)(147,168)
(148,167)(149,166)(150,165)(151,164)(152,163)(153,162)(154,161)(155,160)
(156,159)(170,223)(171,222)(172,234)(173,233)(174,232)(175,231)(176,230)
(177,229)(178,228)(179,227)(180,226)(181,225)(182,224)(183,184)(185,195)
(186,194)(187,193)(188,192)(189,191)(209,210)(211,221)(212,220)(213,219)
(214,218)(215,217);;
s2 := (  1,131)(  2,132)(  3,133)(  4,134)(  5,135)(  6,136)(  7,137)(  8,138)
(  9,139)( 10,140)( 11,141)( 12,142)( 13,143)( 14,118)( 15,119)( 16,120)
( 17,121)( 18,122)( 19,123)( 20,124)( 21,125)( 22,126)( 23,127)( 24,128)
( 25,129)( 26,130)( 27,144)( 28,145)( 29,146)( 30,147)( 31,148)( 32,149)
( 33,150)( 34,151)( 35,152)( 36,153)( 37,154)( 38,155)( 39,156)( 40,209)
( 41,210)( 42,211)( 43,212)( 44,213)( 45,214)( 46,215)( 47,216)( 48,217)
( 49,218)( 50,219)( 51,220)( 52,221)( 53,196)( 54,197)( 55,198)( 56,199)
( 57,200)( 58,201)( 59,202)( 60,203)( 61,204)( 62,205)( 63,206)( 64,207)
( 65,208)( 66,222)( 67,223)( 68,224)( 69,225)( 70,226)( 71,227)( 72,228)
( 73,229)( 74,230)( 75,231)( 76,232)( 77,233)( 78,234)( 79,170)( 80,171)
( 81,172)( 82,173)( 83,174)( 84,175)( 85,176)( 86,177)( 87,178)( 88,179)
( 89,180)( 90,181)( 91,182)( 92,157)( 93,158)( 94,159)( 95,160)( 96,161)
( 97,162)( 98,163)( 99,164)(100,165)(101,166)(102,167)(103,168)(104,169)
(105,183)(106,184)(107,185)(108,186)(109,187)(110,188)(111,189)(112,190)
(113,191)(114,192)(115,193)(116,194)(117,195);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s0*s1*s2*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*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope