Polytope of Type {126,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {126,4}*1008a
Also Known As : {126,4|2}. if this polytope has another name.
Group : SmallGroup(1008,207)
Rank : 3
Schlafli Type : {126,4}
Number of vertices, edges, etc : 126, 252, 4
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 : {126,2}*504
   3-fold quotients : {42,4}*336a
   4-fold quotients : {63,2}*252
   6-fold quotients : {42,2}*168
   7-fold quotients : {18,4}*144a
   9-fold quotients : {14,4}*112
   12-fold quotients : {21,2}*84
   14-fold quotients : {18,2}*72
   18-fold quotients : {14,2}*56
   21-fold quotients : {6,4}*48a
   28-fold quotients : {9,2}*36
   36-fold quotients : {7,2}*28
   42-fold quotients : {6,2}*24
   63-fold quotients : {2,4}*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)(  4, 19)(  5, 21)(  6, 20)(  7, 16)(  8, 18)(  9, 17)( 10, 13)
( 11, 15)( 12, 14)( 22, 45)( 23, 44)( 24, 43)( 25, 63)( 26, 62)( 27, 61)
( 28, 60)( 29, 59)( 30, 58)( 31, 57)( 32, 56)( 33, 55)( 34, 54)( 35, 53)
( 36, 52)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)( 65, 66)
( 67, 82)( 68, 84)( 69, 83)( 70, 79)( 71, 81)( 72, 80)( 73, 76)( 74, 78)
( 75, 77)( 85,108)( 86,107)( 87,106)( 88,126)( 89,125)( 90,124)( 91,123)
( 92,122)( 93,121)( 94,120)( 95,119)( 96,118)( 97,117)( 98,116)( 99,115)
(100,114)(101,113)(102,112)(103,111)(104,110)(105,109)(128,129)(130,145)
(131,147)(132,146)(133,142)(134,144)(135,143)(136,139)(137,141)(138,140)
(148,171)(149,170)(150,169)(151,189)(152,188)(153,187)(154,186)(155,185)
(156,184)(157,183)(158,182)(159,181)(160,180)(161,179)(162,178)(163,177)
(164,176)(165,175)(166,174)(167,173)(168,172)(191,192)(193,208)(194,210)
(195,209)(196,205)(197,207)(198,206)(199,202)(200,204)(201,203)(211,234)
(212,233)(213,232)(214,252)(215,251)(216,250)(217,249)(218,248)(219,247)
(220,246)(221,245)(222,244)(223,243)(224,242)(225,241)(226,240)(227,239)
(228,238)(229,237)(230,236)(231,235);;
s1 := (  1, 25)(  2, 27)(  3, 26)(  4, 22)(  5, 24)(  6, 23)(  7, 40)(  8, 42)
(  9, 41)( 10, 37)( 11, 39)( 12, 38)( 13, 34)( 14, 36)( 15, 35)( 16, 31)
( 17, 33)( 18, 32)( 19, 28)( 20, 30)( 21, 29)( 43, 48)( 44, 47)( 45, 46)
( 49, 63)( 50, 62)( 51, 61)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 64, 88)
( 65, 90)( 66, 89)( 67, 85)( 68, 87)( 69, 86)( 70,103)( 71,105)( 72,104)
( 73,100)( 74,102)( 75,101)( 76, 97)( 77, 99)( 78, 98)( 79, 94)( 80, 96)
( 81, 95)( 82, 91)( 83, 93)( 84, 92)(106,111)(107,110)(108,109)(112,126)
(113,125)(114,124)(115,123)(116,122)(117,121)(118,120)(127,214)(128,216)
(129,215)(130,211)(131,213)(132,212)(133,229)(134,231)(135,230)(136,226)
(137,228)(138,227)(139,223)(140,225)(141,224)(142,220)(143,222)(144,221)
(145,217)(146,219)(147,218)(148,193)(149,195)(150,194)(151,190)(152,192)
(153,191)(154,208)(155,210)(156,209)(157,205)(158,207)(159,206)(160,202)
(161,204)(162,203)(163,199)(164,201)(165,200)(166,196)(167,198)(168,197)
(169,237)(170,236)(171,235)(172,234)(173,233)(174,232)(175,252)(176,251)
(177,250)(178,249)(179,248)(180,247)(181,246)(182,245)(183,244)(184,243)
(185,242)(186,241)(187,240)(188,239)(189,238);;
s2 := (  1,127)(  2,128)(  3,129)(  4,130)(  5,131)(  6,132)(  7,133)(  8,134)
(  9,135)( 10,136)( 11,137)( 12,138)( 13,139)( 14,140)( 15,141)( 16,142)
( 17,143)( 18,144)( 19,145)( 20,146)( 21,147)( 22,148)( 23,149)( 24,150)
( 25,151)( 26,152)( 27,153)( 28,154)( 29,155)( 30,156)( 31,157)( 32,158)
( 33,159)( 34,160)( 35,161)( 36,162)( 37,163)( 38,164)( 39,165)( 40,166)
( 41,167)( 42,168)( 43,169)( 44,170)( 45,171)( 46,172)( 47,173)( 48,174)
( 49,175)( 50,176)( 51,177)( 52,178)( 53,179)( 54,180)( 55,181)( 56,182)
( 57,183)( 58,184)( 59,185)( 60,186)( 61,187)( 62,188)( 63,189)( 64,190)
( 65,191)( 66,192)( 67,193)( 68,194)( 69,195)( 70,196)( 71,197)( 72,198)
( 73,199)( 74,200)( 75,201)( 76,202)( 77,203)( 78,204)( 79,205)( 80,206)
( 81,207)( 82,208)( 83,209)( 84,210)( 85,211)( 86,212)( 87,213)( 88,214)
( 89,215)( 90,216)( 91,217)( 92,218)( 93,219)( 94,220)( 95,221)( 96,222)
( 97,223)( 98,224)( 99,225)(100,226)(101,227)(102,228)(103,229)(104,230)
(105,231)(106,232)(107,233)(108,234)(109,235)(110,236)(111,237)(112,238)
(113,239)(114,240)(115,241)(116,242)(117,243)(118,244)(119,245)(120,246)
(121,247)(122,248)(123,249)(124,250)(125,251)(126,252);;
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, 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*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*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)(  4, 19)(  5, 21)(  6, 20)(  7, 16)(  8, 18)(  9, 17)
( 10, 13)( 11, 15)( 12, 14)( 22, 45)( 23, 44)( 24, 43)( 25, 63)( 26, 62)
( 27, 61)( 28, 60)( 29, 59)( 30, 58)( 31, 57)( 32, 56)( 33, 55)( 34, 54)
( 35, 53)( 36, 52)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)
( 65, 66)( 67, 82)( 68, 84)( 69, 83)( 70, 79)( 71, 81)( 72, 80)( 73, 76)
( 74, 78)( 75, 77)( 85,108)( 86,107)( 87,106)( 88,126)( 89,125)( 90,124)
( 91,123)( 92,122)( 93,121)( 94,120)( 95,119)( 96,118)( 97,117)( 98,116)
( 99,115)(100,114)(101,113)(102,112)(103,111)(104,110)(105,109)(128,129)
(130,145)(131,147)(132,146)(133,142)(134,144)(135,143)(136,139)(137,141)
(138,140)(148,171)(149,170)(150,169)(151,189)(152,188)(153,187)(154,186)
(155,185)(156,184)(157,183)(158,182)(159,181)(160,180)(161,179)(162,178)
(163,177)(164,176)(165,175)(166,174)(167,173)(168,172)(191,192)(193,208)
(194,210)(195,209)(196,205)(197,207)(198,206)(199,202)(200,204)(201,203)
(211,234)(212,233)(213,232)(214,252)(215,251)(216,250)(217,249)(218,248)
(219,247)(220,246)(221,245)(222,244)(223,243)(224,242)(225,241)(226,240)
(227,239)(228,238)(229,237)(230,236)(231,235);
s1 := Sym(252)!(  1, 25)(  2, 27)(  3, 26)(  4, 22)(  5, 24)(  6, 23)(  7, 40)
(  8, 42)(  9, 41)( 10, 37)( 11, 39)( 12, 38)( 13, 34)( 14, 36)( 15, 35)
( 16, 31)( 17, 33)( 18, 32)( 19, 28)( 20, 30)( 21, 29)( 43, 48)( 44, 47)
( 45, 46)( 49, 63)( 50, 62)( 51, 61)( 52, 60)( 53, 59)( 54, 58)( 55, 57)
( 64, 88)( 65, 90)( 66, 89)( 67, 85)( 68, 87)( 69, 86)( 70,103)( 71,105)
( 72,104)( 73,100)( 74,102)( 75,101)( 76, 97)( 77, 99)( 78, 98)( 79, 94)
( 80, 96)( 81, 95)( 82, 91)( 83, 93)( 84, 92)(106,111)(107,110)(108,109)
(112,126)(113,125)(114,124)(115,123)(116,122)(117,121)(118,120)(127,214)
(128,216)(129,215)(130,211)(131,213)(132,212)(133,229)(134,231)(135,230)
(136,226)(137,228)(138,227)(139,223)(140,225)(141,224)(142,220)(143,222)
(144,221)(145,217)(146,219)(147,218)(148,193)(149,195)(150,194)(151,190)
(152,192)(153,191)(154,208)(155,210)(156,209)(157,205)(158,207)(159,206)
(160,202)(161,204)(162,203)(163,199)(164,201)(165,200)(166,196)(167,198)
(168,197)(169,237)(170,236)(171,235)(172,234)(173,233)(174,232)(175,252)
(176,251)(177,250)(178,249)(179,248)(180,247)(181,246)(182,245)(183,244)
(184,243)(185,242)(186,241)(187,240)(188,239)(189,238);
s2 := Sym(252)!(  1,127)(  2,128)(  3,129)(  4,130)(  5,131)(  6,132)(  7,133)
(  8,134)(  9,135)( 10,136)( 11,137)( 12,138)( 13,139)( 14,140)( 15,141)
( 16,142)( 17,143)( 18,144)( 19,145)( 20,146)( 21,147)( 22,148)( 23,149)
( 24,150)( 25,151)( 26,152)( 27,153)( 28,154)( 29,155)( 30,156)( 31,157)
( 32,158)( 33,159)( 34,160)( 35,161)( 36,162)( 37,163)( 38,164)( 39,165)
( 40,166)( 41,167)( 42,168)( 43,169)( 44,170)( 45,171)( 46,172)( 47,173)
( 48,174)( 49,175)( 50,176)( 51,177)( 52,178)( 53,179)( 54,180)( 55,181)
( 56,182)( 57,183)( 58,184)( 59,185)( 60,186)( 61,187)( 62,188)( 63,189)
( 64,190)( 65,191)( 66,192)( 67,193)( 68,194)( 69,195)( 70,196)( 71,197)
( 72,198)( 73,199)( 74,200)( 75,201)( 76,202)( 77,203)( 78,204)( 79,205)
( 80,206)( 81,207)( 82,208)( 83,209)( 84,210)( 85,211)( 86,212)( 87,213)
( 88,214)( 89,215)( 90,216)( 91,217)( 92,218)( 93,219)( 94,220)( 95,221)
( 96,222)( 97,223)( 98,224)( 99,225)(100,226)(101,227)(102,228)(103,229)
(104,230)(105,231)(106,232)(107,233)(108,234)(109,235)(110,236)(111,237)
(112,238)(113,239)(114,240)(115,241)(116,242)(117,243)(118,244)(119,245)
(120,246)(121,247)(122,248)(123,249)(124,250)(125,251)(126,252);
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, 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*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*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