Polytope of Type {2,62,8}

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

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

to this polytope