Polytope of Type {8,62}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,62}*992
Also Known As : {8,62|2}. if this polytope has another name.
Group : SmallGroup(992,105)
Rank : 3
Schlafli Type : {8,62}
Number of vertices, edges, etc : 8, 248, 62
Order of s₀s₁s₂ : 248
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,62,2} of size 1984
Vertex Figure Of :
   {2,8,62} of size 1984
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,62}*496
   4-fold quotients : {2,62}*248
   8-fold quotients : {2,31}*124
   31-fold quotients : {8,2}*32
   62-fold quotients : {4,2}*16
   124-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,124}*1984a, {16,62}*1984
Permutation Representation (GAP) :

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

References : None.
to this polytope