Polytope of Type {2,8,62}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,62}*1984
if this polytope has a name.
Group : SmallGroup(1984,1317)
Rank : 4
Schlafli Type : {2,8,62}
Number of vertices, edges, etc : 2, 8, 248, 62
Order of s₀s₁s₂s₃ : 248
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   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 : {2,4,62}*992
   4-fold quotients : {2,2,62}*496
   8-fold quotients : {2,2,31}*248
   31-fold quotients : {2,8,2}*64
   62-fold quotients : {2,4,2}*32
   124-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope