Polytope of Type {2,252}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,252}*1008
if this polytope has a name.
Group : SmallGroup(1008,205)
Rank : 3
Schlafli Type : {2,252}
Number of vertices, edges, etc : 2, 252, 252
Order of s₀s₁s₂ : 252
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {2,126}*504
   3-fold quotients : {2,84}*336
   4-fold quotients : {2,63}*252
   6-fold quotients : {2,42}*168
   7-fold quotients : {2,36}*144
   9-fold quotients : {2,28}*112
   12-fold quotients : {2,21}*84
   14-fold quotients : {2,18}*72
   18-fold quotients : {2,14}*56
   21-fold quotients : {2,12}*48
   28-fold quotients : {2,9}*36
   36-fold quotients : {2,7}*28
   42-fold quotients : {2,6}*24
   63-fold quotients : {2,4}*16
   84-fold quotients : {2,3}*12
   126-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  5)(  6, 21)(  7, 23)(  8, 22)(  9, 18)( 10, 20)( 11, 19)( 12, 15)
( 13, 17)( 14, 16)( 24, 46)( 25, 45)( 26, 47)( 27, 64)( 28, 63)( 29, 65)
( 30, 61)( 31, 60)( 32, 62)( 33, 58)( 34, 57)( 35, 59)( 36, 55)( 37, 54)
( 38, 56)( 39, 52)( 40, 51)( 41, 53)( 42, 49)( 43, 48)( 44, 50)( 67, 68)
( 69, 84)( 70, 86)( 71, 85)( 72, 81)( 73, 83)( 74, 82)( 75, 78)( 76, 80)
( 77, 79)( 87,109)( 88,108)( 89,110)( 90,127)( 91,126)( 92,128)( 93,124)
( 94,123)( 95,125)( 96,121)( 97,120)( 98,122)( 99,118)(100,117)(101,119)
(102,115)(103,114)(104,116)(105,112)(106,111)(107,113)(129,192)(130,194)
(131,193)(132,210)(133,212)(134,211)(135,207)(136,209)(137,208)(138,204)
(139,206)(140,205)(141,201)(142,203)(143,202)(144,198)(145,200)(146,199)
(147,195)(148,197)(149,196)(150,235)(151,234)(152,236)(153,253)(154,252)
(155,254)(156,250)(157,249)(158,251)(159,247)(160,246)(161,248)(162,244)
(163,243)(164,245)(165,241)(166,240)(167,242)(168,238)(169,237)(170,239)
(171,214)(172,213)(173,215)(174,232)(175,231)(176,233)(177,229)(178,228)
(179,230)(180,226)(181,225)(182,227)(183,223)(184,222)(185,224)(186,220)
(187,219)(188,221)(189,217)(190,216)(191,218);;
s2 := (  3,153)(  4,155)(  5,154)(  6,150)(  7,152)(  8,151)(  9,168)( 10,170)
( 11,169)( 12,165)( 13,167)( 14,166)( 15,162)( 16,164)( 17,163)( 18,159)
( 19,161)( 20,160)( 21,156)( 22,158)( 23,157)( 24,132)( 25,134)( 26,133)
( 27,129)( 28,131)( 29,130)( 30,147)( 31,149)( 32,148)( 33,144)( 34,146)
( 35,145)( 36,141)( 37,143)( 38,142)( 39,138)( 40,140)( 41,139)( 42,135)
( 43,137)( 44,136)( 45,175)( 46,174)( 47,176)( 48,172)( 49,171)( 50,173)
( 51,190)( 52,189)( 53,191)( 54,187)( 55,186)( 56,188)( 57,184)( 58,183)
( 59,185)( 60,181)( 61,180)( 62,182)( 63,178)( 64,177)( 65,179)( 66,216)
( 67,218)( 68,217)( 69,213)( 70,215)( 71,214)( 72,231)( 73,233)( 74,232)
( 75,228)( 76,230)( 77,229)( 78,225)( 79,227)( 80,226)( 81,222)( 82,224)
( 83,223)( 84,219)( 85,221)( 86,220)( 87,195)( 88,197)( 89,196)( 90,192)
( 91,194)( 92,193)( 93,210)( 94,212)( 95,211)( 96,207)( 97,209)( 98,208)
( 99,204)(100,206)(101,205)(102,201)(103,203)(104,202)(105,198)(106,200)
(107,199)(108,238)(109,237)(110,239)(111,235)(112,234)(113,236)(114,253)
(115,252)(116,254)(117,250)(118,249)(119,251)(120,247)(121,246)(122,248)
(123,244)(124,243)(125,245)(126,241)(127,240)(128,242);;
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*s1*s0*s1, s0*s2*s0*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*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*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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(254)!(1,2);
s1 := Sym(254)!(  4,  5)(  6, 21)(  7, 23)(  8, 22)(  9, 18)( 10, 20)( 11, 19)
( 12, 15)( 13, 17)( 14, 16)( 24, 46)( 25, 45)( 26, 47)( 27, 64)( 28, 63)
( 29, 65)( 30, 61)( 31, 60)( 32, 62)( 33, 58)( 34, 57)( 35, 59)( 36, 55)
( 37, 54)( 38, 56)( 39, 52)( 40, 51)( 41, 53)( 42, 49)( 43, 48)( 44, 50)
( 67, 68)( 69, 84)( 70, 86)( 71, 85)( 72, 81)( 73, 83)( 74, 82)( 75, 78)
( 76, 80)( 77, 79)( 87,109)( 88,108)( 89,110)( 90,127)( 91,126)( 92,128)
( 93,124)( 94,123)( 95,125)( 96,121)( 97,120)( 98,122)( 99,118)(100,117)
(101,119)(102,115)(103,114)(104,116)(105,112)(106,111)(107,113)(129,192)
(130,194)(131,193)(132,210)(133,212)(134,211)(135,207)(136,209)(137,208)
(138,204)(139,206)(140,205)(141,201)(142,203)(143,202)(144,198)(145,200)
(146,199)(147,195)(148,197)(149,196)(150,235)(151,234)(152,236)(153,253)
(154,252)(155,254)(156,250)(157,249)(158,251)(159,247)(160,246)(161,248)
(162,244)(163,243)(164,245)(165,241)(166,240)(167,242)(168,238)(169,237)
(170,239)(171,214)(172,213)(173,215)(174,232)(175,231)(176,233)(177,229)
(178,228)(179,230)(180,226)(181,225)(182,227)(183,223)(184,222)(185,224)
(186,220)(187,219)(188,221)(189,217)(190,216)(191,218);
s2 := Sym(254)!(  3,153)(  4,155)(  5,154)(  6,150)(  7,152)(  8,151)(  9,168)
( 10,170)( 11,169)( 12,165)( 13,167)( 14,166)( 15,162)( 16,164)( 17,163)
( 18,159)( 19,161)( 20,160)( 21,156)( 22,158)( 23,157)( 24,132)( 25,134)
( 26,133)( 27,129)( 28,131)( 29,130)( 30,147)( 31,149)( 32,148)( 33,144)
( 34,146)( 35,145)( 36,141)( 37,143)( 38,142)( 39,138)( 40,140)( 41,139)
( 42,135)( 43,137)( 44,136)( 45,175)( 46,174)( 47,176)( 48,172)( 49,171)
( 50,173)( 51,190)( 52,189)( 53,191)( 54,187)( 55,186)( 56,188)( 57,184)
( 58,183)( 59,185)( 60,181)( 61,180)( 62,182)( 63,178)( 64,177)( 65,179)
( 66,216)( 67,218)( 68,217)( 69,213)( 70,215)( 71,214)( 72,231)( 73,233)
( 74,232)( 75,228)( 76,230)( 77,229)( 78,225)( 79,227)( 80,226)( 81,222)
( 82,224)( 83,223)( 84,219)( 85,221)( 86,220)( 87,195)( 88,197)( 89,196)
( 90,192)( 91,194)( 92,193)( 93,210)( 94,212)( 95,211)( 96,207)( 97,209)
( 98,208)( 99,204)(100,206)(101,205)(102,201)(103,203)(104,202)(105,198)
(106,200)(107,199)(108,238)(109,237)(110,239)(111,235)(112,234)(113,236)
(114,253)(115,252)(116,254)(117,250)(118,249)(119,251)(120,247)(121,246)
(122,248)(123,244)(124,243)(125,245)(126,241)(127,240)(128,242);
poly := sub<Sym(254)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s1*s0*s1, s0*s2*s0*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*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*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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope