Polytope of Type {18,28}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,28}*1008b
if this polytope has a name.
Group : SmallGroup(1008,500)
Rank : 3
Schlafli Type : {18,28}
Number of vertices, edges, etc : 18, 252, 28
Order of s₀s₁s₂ : 63
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-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) :
   3-fold quotients : {6,28}*336b
   7-fold quotients : {18,4}*144c
   14-fold quotients : {9,4}*72
   21-fold quotients : {6,4}*48b
   42-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope