Polytope of Type {62,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {62,8}*992
Also Known As : {62,8|2}. if this polytope has another name.
Group : SmallGroup(992,105)
Rank : 3
Schlafli Type : {62,8}
Number of vertices, edges, etc : 62, 248, 8
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 :
{62,8,2} of size 1984
Vertex Figure Of :
{2,62,8} of size 1984
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {62,4}*496
4-fold quotients : {62,2}*248
8-fold quotients : {31,2}*124
31-fold quotients : {2,8}*32
62-fold quotients : {2,4}*16
124-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {124,8}*1984a, {62,16}*1984
Permutation Representation (GAP) :
s0 := ( 2, 31)( 3, 30)( 4, 29)( 5, 28)( 6, 27)( 7, 26)( 8, 25)( 9, 24)
( 10, 23)( 11, 22)( 12, 21)( 13, 20)( 14, 19)( 15, 18)( 16, 17)( 33, 62)
( 34, 61)( 35, 60)( 36, 59)( 37, 58)( 38, 57)( 39, 56)( 40, 55)( 41, 54)
( 42, 53)( 43, 52)( 44, 51)( 45, 50)( 46, 49)( 47, 48)( 64, 93)( 65, 92)
( 66, 91)( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71, 86)( 72, 85)( 73, 84)
( 74, 83)( 75, 82)( 76, 81)( 77, 80)( 78, 79)( 95,124)( 96,123)( 97,122)
( 98,121)( 99,120)(100,119)(101,118)(102,117)(103,116)(104,115)(105,114)
(106,113)(107,112)(108,111)(109,110)(126,155)(127,154)(128,153)(129,152)
(130,151)(131,150)(132,149)(133,148)(134,147)(135,146)(136,145)(137,144)
(138,143)(139,142)(140,141)(157,186)(158,185)(159,184)(160,183)(161,182)
(162,181)(163,180)(164,179)(165,178)(166,177)(167,176)(168,175)(169,174)
(170,173)(171,172)(188,217)(189,216)(190,215)(191,214)(192,213)(193,212)
(194,211)(195,210)(196,209)(197,208)(198,207)(199,206)(200,205)(201,204)
(202,203)(219,248)(220,247)(221,246)(222,245)(223,244)(224,243)(225,242)
(226,241)(227,240)(228,239)(229,238)(230,237)(231,236)(232,235)(233,234);;
s1 := ( 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, 95)( 64, 94)
( 65,124)( 66,123)( 67,122)( 68,121)( 69,120)( 70,119)( 71,118)( 72,117)
( 73,116)( 74,115)( 75,114)( 76,113)( 77,112)( 78,111)( 79,110)( 80,109)
( 81,108)( 82,107)( 83,106)( 84,105)( 85,104)( 86,103)( 87,102)( 88,101)
( 89,100)( 90, 99)( 91, 98)( 92, 97)( 93, 96)(125,188)(126,187)(127,217)
(128,216)(129,215)(130,214)(131,213)(132,212)(133,211)(134,210)(135,209)
(136,208)(137,207)(138,206)(139,205)(140,204)(141,203)(142,202)(143,201)
(144,200)(145,199)(146,198)(147,197)(148,196)(149,195)(150,194)(151,193)
(152,192)(153,191)(154,190)(155,189)(156,219)(157,218)(158,248)(159,247)
(160,246)(161,245)(162,244)(163,243)(164,242)(165,241)(166,240)(167,239)
(168,238)(169,237)(170,236)(171,235)(172,234)(173,233)(174,232)(175,231)
(176,230)(177,229)(178,228)(179,227)(180,226)(181,225)(182,224)(183,223)
(184,222)(185,221)(186,220);;
s2 := ( 1,125)( 2,126)( 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)( 63,218)( 64,219)
( 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)( 94,187)( 95,188)( 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);;
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*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(248)!( 2, 31)( 3, 30)( 4, 29)( 5, 28)( 6, 27)( 7, 26)( 8, 25)
( 9, 24)( 10, 23)( 11, 22)( 12, 21)( 13, 20)( 14, 19)( 15, 18)( 16, 17)
( 33, 62)( 34, 61)( 35, 60)( 36, 59)( 37, 58)( 38, 57)( 39, 56)( 40, 55)
( 41, 54)( 42, 53)( 43, 52)( 44, 51)( 45, 50)( 46, 49)( 47, 48)( 64, 93)
( 65, 92)( 66, 91)( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71, 86)( 72, 85)
( 73, 84)( 74, 83)( 75, 82)( 76, 81)( 77, 80)( 78, 79)( 95,124)( 96,123)
( 97,122)( 98,121)( 99,120)(100,119)(101,118)(102,117)(103,116)(104,115)
(105,114)(106,113)(107,112)(108,111)(109,110)(126,155)(127,154)(128,153)
(129,152)(130,151)(131,150)(132,149)(133,148)(134,147)(135,146)(136,145)
(137,144)(138,143)(139,142)(140,141)(157,186)(158,185)(159,184)(160,183)
(161,182)(162,181)(163,180)(164,179)(165,178)(166,177)(167,176)(168,175)
(169,174)(170,173)(171,172)(188,217)(189,216)(190,215)(191,214)(192,213)
(193,212)(194,211)(195,210)(196,209)(197,208)(198,207)(199,206)(200,205)
(201,204)(202,203)(219,248)(220,247)(221,246)(222,245)(223,244)(224,243)
(225,242)(226,241)(227,240)(228,239)(229,238)(230,237)(231,236)(232,235)
(233,234);
s1 := 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, 95)
( 64, 94)( 65,124)( 66,123)( 67,122)( 68,121)( 69,120)( 70,119)( 71,118)
( 72,117)( 73,116)( 74,115)( 75,114)( 76,113)( 77,112)( 78,111)( 79,110)
( 80,109)( 81,108)( 82,107)( 83,106)( 84,105)( 85,104)( 86,103)( 87,102)
( 88,101)( 89,100)( 90, 99)( 91, 98)( 92, 97)( 93, 96)(125,188)(126,187)
(127,217)(128,216)(129,215)(130,214)(131,213)(132,212)(133,211)(134,210)
(135,209)(136,208)(137,207)(138,206)(139,205)(140,204)(141,203)(142,202)
(143,201)(144,200)(145,199)(146,198)(147,197)(148,196)(149,195)(150,194)
(151,193)(152,192)(153,191)(154,190)(155,189)(156,219)(157,218)(158,248)
(159,247)(160,246)(161,245)(162,244)(163,243)(164,242)(165,241)(166,240)
(167,239)(168,238)(169,237)(170,236)(171,235)(172,234)(173,233)(174,232)
(175,231)(176,230)(177,229)(178,228)(179,227)(180,226)(181,225)(182,224)
(183,223)(184,222)(185,221)(186,220);
s2 := Sym(248)!( 1,125)( 2,126)( 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)( 63,218)
( 64,219)( 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)( 94,187)( 95,188)
( 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);
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,
s1*s2*s1*s2*s1*s2*s1*s2*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 >;
References : None.
to this polytope