Polytope of Type {2,4,63}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,63}*1008
if this polytope has a name.
Group : SmallGroup(1008,503)
Rank : 4
Schlafli Type : {2,4,63}
Number of vertices, edges, etc : 2, 4, 126, 63
Order of s₀s₁s₂s₃ : 126
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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) :
   3-fold quotients : {2,4,21}*336
   7-fold quotients : {2,4,9}*144
   21-fold quotients : {2,4,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  3,  5)(  4,  6)(  7,  9)(  8, 10)( 11, 13)( 12, 14)( 15, 17)( 16, 18)
( 19, 21)( 20, 22)( 23, 25)( 24, 26)( 27, 29)( 28, 30)( 31, 33)( 32, 34)
( 35, 37)( 36, 38)( 39, 41)( 40, 42)( 43, 45)( 44, 46)( 47, 49)( 48, 50)
( 51, 53)( 52, 54)( 55, 57)( 56, 58)( 59, 61)( 60, 62)( 63, 65)( 64, 66)
( 67, 69)( 68, 70)( 71, 73)( 72, 74)( 75, 77)( 76, 78)( 79, 81)( 80, 82)
( 83, 85)( 84, 86)( 87, 89)( 88, 90)( 91, 93)( 92, 94)( 95, 97)( 96, 98)
( 99,101)(100,102)(103,105)(104,106)(107,109)(108,110)(111,113)(112,114)
(115,117)(116,118)(119,121)(120,122)(123,125)(124,126)(127,129)(128,130)
(131,133)(132,134)(135,137)(136,138)(139,141)(140,142)(143,145)(144,146)
(147,149)(148,150)(151,153)(152,154)(155,157)(156,158)(159,161)(160,162)
(163,165)(164,166)(167,169)(168,170)(171,173)(172,174)(175,177)(176,178)
(179,181)(180,182)(183,185)(184,186)(187,189)(188,190)(191,193)(192,194)
(195,197)(196,198)(199,201)(200,202)(203,205)(204,206)(207,209)(208,210)
(211,213)(212,214)(215,217)(216,218)(219,221)(220,222)(223,225)(224,226)
(227,229)(228,230)(231,233)(232,234)(235,237)(236,238)(239,241)(240,242)
(243,245)(244,246)(247,249)(248,250)(251,253)(252,254);;
s2 := (  4,  5)(  7, 11)(  8, 13)(  9, 12)( 10, 14)( 15, 75)( 16, 77)( 17, 76)
( 18, 78)( 19, 83)( 20, 85)( 21, 84)( 22, 86)( 23, 79)( 24, 81)( 25, 80)
( 26, 82)( 27, 63)( 28, 65)( 29, 64)( 30, 66)( 31, 71)( 32, 73)( 33, 72)
( 34, 74)( 35, 67)( 36, 69)( 37, 68)( 38, 70)( 39, 51)( 40, 53)( 41, 52)
( 42, 54)( 43, 59)( 44, 61)( 45, 60)( 46, 62)( 47, 55)( 48, 57)( 49, 56)
( 50, 58)( 87,175)( 88,177)( 89,176)( 90,178)( 91,171)( 92,173)( 93,172)
( 94,174)( 95,179)( 96,181)( 97,180)( 98,182)( 99,247)(100,249)(101,248)
(102,250)(103,243)(104,245)(105,244)(106,246)(107,251)(108,253)(109,252)
(110,254)(111,235)(112,237)(113,236)(114,238)(115,231)(116,233)(117,232)
(118,234)(119,239)(120,241)(121,240)(122,242)(123,223)(124,225)(125,224)
(126,226)(127,219)(128,221)(129,220)(130,222)(131,227)(132,229)(133,228)
(134,230)(135,211)(136,213)(137,212)(138,214)(139,207)(140,209)(141,208)
(142,210)(143,215)(144,217)(145,216)(146,218)(147,199)(148,201)(149,200)
(150,202)(151,195)(152,197)(153,196)(154,198)(155,203)(156,205)(157,204)
(158,206)(159,187)(160,189)(161,188)(162,190)(163,183)(164,185)(165,184)
(166,186)(167,191)(168,193)(169,192)(170,194);;
s3 := (  3,183)(  4,186)(  5,185)(  6,184)(  7,191)(  8,194)(  9,193)( 10,192)
( 11,187)( 12,190)( 13,189)( 14,188)( 15,171)( 16,174)( 17,173)( 18,172)
( 19,179)( 20,182)( 21,181)( 22,180)( 23,175)( 24,178)( 25,177)( 26,176)
( 27,243)( 28,246)( 29,245)( 30,244)( 31,251)( 32,254)( 33,253)( 34,252)
( 35,247)( 36,250)( 37,249)( 38,248)( 39,231)( 40,234)( 41,233)( 42,232)
( 43,239)( 44,242)( 45,241)( 46,240)( 47,235)( 48,238)( 49,237)( 50,236)
( 51,219)( 52,222)( 53,221)( 54,220)( 55,227)( 56,230)( 57,229)( 58,228)
( 59,223)( 60,226)( 61,225)( 62,224)( 63,207)( 64,210)( 65,209)( 66,208)
( 67,215)( 68,218)( 69,217)( 70,216)( 71,211)( 72,214)( 73,213)( 74,212)
( 75,195)( 76,198)( 77,197)( 78,196)( 79,203)( 80,206)( 81,205)( 82,204)
( 83,199)( 84,202)( 85,201)( 86,200)( 87, 99)( 88,102)( 89,101)( 90,100)
( 91,107)( 92,110)( 93,109)( 94,108)( 95,103)( 96,106)( 97,105)( 98,104)
(111,159)(112,162)(113,161)(114,160)(115,167)(116,170)(117,169)(118,168)
(119,163)(120,166)(121,165)(122,164)(123,147)(124,150)(125,149)(126,148)
(127,155)(128,158)(129,157)(130,156)(131,151)(132,154)(133,153)(134,152)
(136,138)(139,143)(140,146)(141,145)(142,144);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(254)!(1,2);
s1 := Sym(254)!(  3,  5)(  4,  6)(  7,  9)(  8, 10)( 11, 13)( 12, 14)( 15, 17)
( 16, 18)( 19, 21)( 20, 22)( 23, 25)( 24, 26)( 27, 29)( 28, 30)( 31, 33)
( 32, 34)( 35, 37)( 36, 38)( 39, 41)( 40, 42)( 43, 45)( 44, 46)( 47, 49)
( 48, 50)( 51, 53)( 52, 54)( 55, 57)( 56, 58)( 59, 61)( 60, 62)( 63, 65)
( 64, 66)( 67, 69)( 68, 70)( 71, 73)( 72, 74)( 75, 77)( 76, 78)( 79, 81)
( 80, 82)( 83, 85)( 84, 86)( 87, 89)( 88, 90)( 91, 93)( 92, 94)( 95, 97)
( 96, 98)( 99,101)(100,102)(103,105)(104,106)(107,109)(108,110)(111,113)
(112,114)(115,117)(116,118)(119,121)(120,122)(123,125)(124,126)(127,129)
(128,130)(131,133)(132,134)(135,137)(136,138)(139,141)(140,142)(143,145)
(144,146)(147,149)(148,150)(151,153)(152,154)(155,157)(156,158)(159,161)
(160,162)(163,165)(164,166)(167,169)(168,170)(171,173)(172,174)(175,177)
(176,178)(179,181)(180,182)(183,185)(184,186)(187,189)(188,190)(191,193)
(192,194)(195,197)(196,198)(199,201)(200,202)(203,205)(204,206)(207,209)
(208,210)(211,213)(212,214)(215,217)(216,218)(219,221)(220,222)(223,225)
(224,226)(227,229)(228,230)(231,233)(232,234)(235,237)(236,238)(239,241)
(240,242)(243,245)(244,246)(247,249)(248,250)(251,253)(252,254);
s2 := Sym(254)!(  4,  5)(  7, 11)(  8, 13)(  9, 12)( 10, 14)( 15, 75)( 16, 77)
( 17, 76)( 18, 78)( 19, 83)( 20, 85)( 21, 84)( 22, 86)( 23, 79)( 24, 81)
( 25, 80)( 26, 82)( 27, 63)( 28, 65)( 29, 64)( 30, 66)( 31, 71)( 32, 73)
( 33, 72)( 34, 74)( 35, 67)( 36, 69)( 37, 68)( 38, 70)( 39, 51)( 40, 53)
( 41, 52)( 42, 54)( 43, 59)( 44, 61)( 45, 60)( 46, 62)( 47, 55)( 48, 57)
( 49, 56)( 50, 58)( 87,175)( 88,177)( 89,176)( 90,178)( 91,171)( 92,173)
( 93,172)( 94,174)( 95,179)( 96,181)( 97,180)( 98,182)( 99,247)(100,249)
(101,248)(102,250)(103,243)(104,245)(105,244)(106,246)(107,251)(108,253)
(109,252)(110,254)(111,235)(112,237)(113,236)(114,238)(115,231)(116,233)
(117,232)(118,234)(119,239)(120,241)(121,240)(122,242)(123,223)(124,225)
(125,224)(126,226)(127,219)(128,221)(129,220)(130,222)(131,227)(132,229)
(133,228)(134,230)(135,211)(136,213)(137,212)(138,214)(139,207)(140,209)
(141,208)(142,210)(143,215)(144,217)(145,216)(146,218)(147,199)(148,201)
(149,200)(150,202)(151,195)(152,197)(153,196)(154,198)(155,203)(156,205)
(157,204)(158,206)(159,187)(160,189)(161,188)(162,190)(163,183)(164,185)
(165,184)(166,186)(167,191)(168,193)(169,192)(170,194);
s3 := Sym(254)!(  3,183)(  4,186)(  5,185)(  6,184)(  7,191)(  8,194)(  9,193)
( 10,192)( 11,187)( 12,190)( 13,189)( 14,188)( 15,171)( 16,174)( 17,173)
( 18,172)( 19,179)( 20,182)( 21,181)( 22,180)( 23,175)( 24,178)( 25,177)
( 26,176)( 27,243)( 28,246)( 29,245)( 30,244)( 31,251)( 32,254)( 33,253)
( 34,252)( 35,247)( 36,250)( 37,249)( 38,248)( 39,231)( 40,234)( 41,233)
( 42,232)( 43,239)( 44,242)( 45,241)( 46,240)( 47,235)( 48,238)( 49,237)
( 50,236)( 51,219)( 52,222)( 53,221)( 54,220)( 55,227)( 56,230)( 57,229)
( 58,228)( 59,223)( 60,226)( 61,225)( 62,224)( 63,207)( 64,210)( 65,209)
( 66,208)( 67,215)( 68,218)( 69,217)( 70,216)( 71,211)( 72,214)( 73,213)
( 74,212)( 75,195)( 76,198)( 77,197)( 78,196)( 79,203)( 80,206)( 81,205)
( 82,204)( 83,199)( 84,202)( 85,201)( 86,200)( 87, 99)( 88,102)( 89,101)
( 90,100)( 91,107)( 92,110)( 93,109)( 94,108)( 95,103)( 96,106)( 97,105)
( 98,104)(111,159)(112,162)(113,161)(114,160)(115,167)(116,170)(117,169)
(118,168)(119,163)(120,166)(121,165)(122,164)(123,147)(124,150)(125,149)
(126,148)(127,155)(128,158)(129,157)(130,156)(131,151)(132,154)(133,153)
(134,152)(136,138)(139,143)(140,146)(141,145)(142,144);
poly := sub<Sym(254)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope