Polytope of Type {36,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {36,14}*1008
Also Known As : {36,14|2}. if this polytope has another name.
Group : SmallGroup(1008,157)
Rank : 3
Schlafli Type : {36,14}
Number of vertices, edges, etc : 36, 252, 14
Order of s₀s₁s₂ : 252
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 : {18,14}*504
   3-fold quotients : {12,14}*336
   6-fold quotients : {6,14}*168
   7-fold quotients : {36,2}*144
   9-fold quotients : {4,14}*112
   14-fold quotients : {18,2}*72
   18-fold quotients : {2,14}*56
   21-fold quotients : {12,2}*48
   28-fold quotients : {9,2}*36
   36-fold quotients : {2,7}*28
   42-fold quotients : {6,2}*24
   63-fold quotients : {4,2}*16
   84-fold quotients : {3,2}*12
   126-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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