Polytope of Type {248}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {248}*496
Also Known As : 248-gon, {248}. if this polytope has another name.
Group : SmallGroup(496,6)
Rank : 2
Schlafli Type : {248}
Number of vertices, edges, etc : 248, 248
Order of s0s1 : 248
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{248,2} of size 992
{248,4} of size 1984
{248,4} of size 1984
Vertex Figure Of :
{2,248} of size 992
{4,248} of size 1984
{4,248} of size 1984
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {124}*248
4-fold quotients : {62}*124
8-fold quotients : {31}*62
31-fold quotients : {8}*16
62-fold quotients : {4}*8
124-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {496}*992
3-fold covers : {744}*1488
4-fold covers : {992}*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)( 63, 94)( 64,124)
( 65,123)( 66,122)( 67,121)( 68,120)( 69,119)( 70,118)( 71,117)( 72,116)
( 73,115)( 74,114)( 75,113)( 76,112)( 77,111)( 78,110)( 79,109)( 80,108)
( 81,107)( 82,106)( 83,105)( 84,104)( 85,103)( 86,102)( 87,101)( 88,100)
( 89, 99)( 90, 98)( 91, 97)( 92, 96)( 93, 95)(125,187)(126,217)(127,216)
(128,215)(129,214)(130,213)(131,212)(132,211)(133,210)(134,209)(135,208)
(136,207)(137,206)(138,205)(139,204)(140,203)(141,202)(142,201)(143,200)
(144,199)(145,198)(146,197)(147,196)(148,195)(149,194)(150,193)(151,192)
(152,191)(153,190)(154,189)(155,188)(156,218)(157,248)(158,247)(159,246)
(160,245)(161,244)(162,243)(163,242)(164,241)(165,240)(166,239)(167,238)
(168,237)(169,236)(170,235)(171,234)(172,233)(173,232)(174,231)(175,230)
(176,229)(177,228)(178,227)(179,226)(180,225)(181,224)(182,223)(183,222)
(184,221)(185,220)(186,219);;
s1 := ( 1,126)( 2,125)( 3,155)( 4,154)( 5,153)( 6,152)( 7,151)( 8,150)
( 9,149)( 10,148)( 11,147)( 12,146)( 13,145)( 14,144)( 15,143)( 16,142)
( 17,141)( 18,140)( 19,139)( 20,138)( 21,137)( 22,136)( 23,135)( 24,134)
( 25,133)( 26,132)( 27,131)( 28,130)( 29,129)( 30,128)( 31,127)( 32,157)
( 33,156)( 34,186)( 35,185)( 36,184)( 37,183)( 38,182)( 39,181)( 40,180)
( 41,179)( 42,178)( 43,177)( 44,176)( 45,175)( 46,174)( 47,173)( 48,172)
( 49,171)( 50,170)( 51,169)( 52,168)( 53,167)( 54,166)( 55,165)( 56,164)
( 57,163)( 58,162)( 59,161)( 60,160)( 61,159)( 62,158)( 63,219)( 64,218)
( 65,248)( 66,247)( 67,246)( 68,245)( 69,244)( 70,243)( 71,242)( 72,241)
( 73,240)( 74,239)( 75,238)( 76,237)( 77,236)( 78,235)( 79,234)( 80,233)
( 81,232)( 82,231)( 83,230)( 84,229)( 85,228)( 86,227)( 87,226)( 88,225)
( 89,224)( 90,223)( 91,222)( 92,221)( 93,220)( 94,188)( 95,187)( 96,217)
( 97,216)( 98,215)( 99,214)(100,213)(101,212)(102,211)(103,210)(104,209)
(105,208)(106,207)(107,206)(108,205)(109,204)(110,203)(111,202)(112,201)
(113,200)(114,199)(115,198)(116,197)(117,196)(118,195)(119,194)(120,193)
(121,192)(122,191)(123,190)(124,189);;
poly := Group([s0,s1]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;; s1 := F.2;;
rels := [ s0*s0, s1*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*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*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*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*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)( 63, 94)
( 64,124)( 65,123)( 66,122)( 67,121)( 68,120)( 69,119)( 70,118)( 71,117)
( 72,116)( 73,115)( 74,114)( 75,113)( 76,112)( 77,111)( 78,110)( 79,109)
( 80,108)( 81,107)( 82,106)( 83,105)( 84,104)( 85,103)( 86,102)( 87,101)
( 88,100)( 89, 99)( 90, 98)( 91, 97)( 92, 96)( 93, 95)(125,187)(126,217)
(127,216)(128,215)(129,214)(130,213)(131,212)(132,211)(133,210)(134,209)
(135,208)(136,207)(137,206)(138,205)(139,204)(140,203)(141,202)(142,201)
(143,200)(144,199)(145,198)(146,197)(147,196)(148,195)(149,194)(150,193)
(151,192)(152,191)(153,190)(154,189)(155,188)(156,218)(157,248)(158,247)
(159,246)(160,245)(161,244)(162,243)(163,242)(164,241)(165,240)(166,239)
(167,238)(168,237)(169,236)(170,235)(171,234)(172,233)(173,232)(174,231)
(175,230)(176,229)(177,228)(178,227)(179,226)(180,225)(181,224)(182,223)
(183,222)(184,221)(185,220)(186,219);
s1 := Sym(248)!( 1,126)( 2,125)( 3,155)( 4,154)( 5,153)( 6,152)( 7,151)
( 8,150)( 9,149)( 10,148)( 11,147)( 12,146)( 13,145)( 14,144)( 15,143)
( 16,142)( 17,141)( 18,140)( 19,139)( 20,138)( 21,137)( 22,136)( 23,135)
( 24,134)( 25,133)( 26,132)( 27,131)( 28,130)( 29,129)( 30,128)( 31,127)
( 32,157)( 33,156)( 34,186)( 35,185)( 36,184)( 37,183)( 38,182)( 39,181)
( 40,180)( 41,179)( 42,178)( 43,177)( 44,176)( 45,175)( 46,174)( 47,173)
( 48,172)( 49,171)( 50,170)( 51,169)( 52,168)( 53,167)( 54,166)( 55,165)
( 56,164)( 57,163)( 58,162)( 59,161)( 60,160)( 61,159)( 62,158)( 63,219)
( 64,218)( 65,248)( 66,247)( 67,246)( 68,245)( 69,244)( 70,243)( 71,242)
( 72,241)( 73,240)( 74,239)( 75,238)( 76,237)( 77,236)( 78,235)( 79,234)
( 80,233)( 81,232)( 82,231)( 83,230)( 84,229)( 85,228)( 86,227)( 87,226)
( 88,225)( 89,224)( 90,223)( 91,222)( 92,221)( 93,220)( 94,188)( 95,187)
( 96,217)( 97,216)( 98,215)( 99,214)(100,213)(101,212)(102,211)(103,210)
(104,209)(105,208)(106,207)(107,206)(108,205)(109,204)(110,203)(111,202)
(112,201)(113,200)(114,199)(115,198)(116,197)(117,196)(118,195)(119,194)
(120,193)(121,192)(122,191)(123,190)(124,189);
poly := sub<Sym(248)|s0,s1>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*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*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*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*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*s0*s1 >;
References : None.
to this polytope