Polytope of Type {14,36}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope