Polytope of Type {246,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {246,2}*984
if this polytope has a name.
Group : SmallGroup(984,45)
Rank : 3
Schlafli Type : {246,2}
Number of vertices, edges, etc : 246, 246, 2
Order of s₀s₁s₂ : 246
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {246,2,2} of size 1968
Vertex Figure Of :
   {2,246,2} of size 1968
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {123,2}*492
   3-fold quotients : {82,2}*328
   6-fold quotients : {41,2}*164
   41-fold quotients : {6,2}*24
   82-fold quotients : {3,2}*12
   123-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {492,2}*1968, {246,4}*1968a
Permutation Representation (GAP) :

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

to this polytope