Polytope of Type {2,12,38}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,38}*1824
if this polytope has a name.
Group : SmallGroup(1824,1131)
Rank : 4
Schlafli Type : {2,12,38}
Number of vertices, edges, etc : 2, 12, 228, 38
Order of s₀s₁s₂s₃ : 228
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   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 : {2,6,38}*912
   3-fold quotients : {2,4,38}*608
   6-fold quotients : {2,2,38}*304
   12-fold quotients : {2,2,19}*152
   19-fold quotients : {2,12,2}*96
   38-fold quotients : {2,6,2}*48
   57-fold quotients : {2,4,2}*32
   76-fold quotients : {2,3,2}*24
   114-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 22, 41)( 23, 42)( 24, 43)( 25, 44)( 26, 45)( 27, 46)( 28, 47)( 29, 48)
( 30, 49)( 31, 50)( 32, 51)( 33, 52)( 34, 53)( 35, 54)( 36, 55)( 37, 56)
( 38, 57)( 39, 58)( 40, 59)( 79, 98)( 80, 99)( 81,100)( 82,101)( 83,102)
( 84,103)( 85,104)( 86,105)( 87,106)( 88,107)( 89,108)( 90,109)( 91,110)
( 92,111)( 93,112)( 94,113)( 95,114)( 96,115)( 97,116)(117,174)(118,175)
(119,176)(120,177)(121,178)(122,179)(123,180)(124,181)(125,182)(126,183)
(127,184)(128,185)(129,186)(130,187)(131,188)(132,189)(133,190)(134,191)
(135,192)(136,212)(137,213)(138,214)(139,215)(140,216)(141,217)(142,218)
(143,219)(144,220)(145,221)(146,222)(147,223)(148,224)(149,225)(150,226)
(151,227)(152,228)(153,229)(154,230)(155,193)(156,194)(157,195)(158,196)
(159,197)(160,198)(161,199)(162,200)(163,201)(164,202)(165,203)(166,204)
(167,205)(168,206)(169,207)(170,208)(171,209)(172,210)(173,211);;
s2 := (  3,136)(  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)( 22,117)( 23,135)( 24,134)( 25,133)( 26,132)
( 27,131)( 28,130)( 29,129)( 30,128)( 31,127)( 32,126)( 33,125)( 34,124)
( 35,123)( 36,122)( 37,121)( 38,120)( 39,119)( 40,118)( 41,155)( 42,173)
( 43,172)( 44,171)( 45,170)( 46,169)( 47,168)( 48,167)( 49,166)( 50,165)
( 51,164)( 52,163)( 53,162)( 54,161)( 55,160)( 56,159)( 57,158)( 58,157)
( 59,156)( 60,193)( 61,211)( 62,210)( 63,209)( 64,208)( 65,207)( 66,206)
( 67,205)( 68,204)( 69,203)( 70,202)( 71,201)( 72,200)( 73,199)( 74,198)
( 75,197)( 76,196)( 77,195)( 78,194)( 79,174)( 80,192)( 81,191)( 82,190)
( 83,189)( 84,188)( 85,187)( 86,186)( 87,185)( 88,184)( 89,183)( 90,182)
( 91,181)( 92,180)( 93,179)( 94,178)( 95,177)( 96,176)( 97,175)( 98,212)
( 99,230)(100,229)(101,228)(102,227)(103,226)(104,225)(105,224)(106,223)
(107,222)(108,221)(109,220)(110,219)(111,218)(112,217)(113,216)(114,215)
(115,214)(116,213);;
s3 := (  3,  4)(  5, 21)(  6, 20)(  7, 19)(  8, 18)(  9, 17)( 10, 16)( 11, 15)
( 12, 14)( 22, 23)( 24, 40)( 25, 39)( 26, 38)( 27, 37)( 28, 36)( 29, 35)
( 30, 34)( 31, 33)( 41, 42)( 43, 59)( 44, 58)( 45, 57)( 46, 56)( 47, 55)
( 48, 54)( 49, 53)( 50, 52)( 60, 61)( 62, 78)( 63, 77)( 64, 76)( 65, 75)
( 66, 74)( 67, 73)( 68, 72)( 69, 71)( 79, 80)( 81, 97)( 82, 96)( 83, 95)
( 84, 94)( 85, 93)( 86, 92)( 87, 91)( 88, 90)( 98, 99)(100,116)(101,115)
(102,114)(103,113)(104,112)(105,111)(106,110)(107,109)(117,118)(119,135)
(120,134)(121,133)(122,132)(123,131)(124,130)(125,129)(126,128)(136,137)
(138,154)(139,153)(140,152)(141,151)(142,150)(143,149)(144,148)(145,147)
(155,156)(157,173)(158,172)(159,171)(160,170)(161,169)(162,168)(163,167)
(164,166)(174,175)(176,192)(177,191)(178,190)(179,189)(180,188)(181,187)
(182,186)(183,185)(193,194)(195,211)(196,210)(197,209)(198,208)(199,207)
(200,206)(201,205)(202,204)(212,213)(214,230)(215,229)(216,228)(217,227)
(218,226)(219,225)(220,224)(221,223);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(230)!(1,2);
s1 := Sym(230)!( 22, 41)( 23, 42)( 24, 43)( 25, 44)( 26, 45)( 27, 46)( 28, 47)
( 29, 48)( 30, 49)( 31, 50)( 32, 51)( 33, 52)( 34, 53)( 35, 54)( 36, 55)
( 37, 56)( 38, 57)( 39, 58)( 40, 59)( 79, 98)( 80, 99)( 81,100)( 82,101)
( 83,102)( 84,103)( 85,104)( 86,105)( 87,106)( 88,107)( 89,108)( 90,109)
( 91,110)( 92,111)( 93,112)( 94,113)( 95,114)( 96,115)( 97,116)(117,174)
(118,175)(119,176)(120,177)(121,178)(122,179)(123,180)(124,181)(125,182)
(126,183)(127,184)(128,185)(129,186)(130,187)(131,188)(132,189)(133,190)
(134,191)(135,192)(136,212)(137,213)(138,214)(139,215)(140,216)(141,217)
(142,218)(143,219)(144,220)(145,221)(146,222)(147,223)(148,224)(149,225)
(150,226)(151,227)(152,228)(153,229)(154,230)(155,193)(156,194)(157,195)
(158,196)(159,197)(160,198)(161,199)(162,200)(163,201)(164,202)(165,203)
(166,204)(167,205)(168,206)(169,207)(170,208)(171,209)(172,210)(173,211);
s2 := Sym(230)!(  3,136)(  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)( 22,117)( 23,135)( 24,134)( 25,133)
( 26,132)( 27,131)( 28,130)( 29,129)( 30,128)( 31,127)( 32,126)( 33,125)
( 34,124)( 35,123)( 36,122)( 37,121)( 38,120)( 39,119)( 40,118)( 41,155)
( 42,173)( 43,172)( 44,171)( 45,170)( 46,169)( 47,168)( 48,167)( 49,166)
( 50,165)( 51,164)( 52,163)( 53,162)( 54,161)( 55,160)( 56,159)( 57,158)
( 58,157)( 59,156)( 60,193)( 61,211)( 62,210)( 63,209)( 64,208)( 65,207)
( 66,206)( 67,205)( 68,204)( 69,203)( 70,202)( 71,201)( 72,200)( 73,199)
( 74,198)( 75,197)( 76,196)( 77,195)( 78,194)( 79,174)( 80,192)( 81,191)
( 82,190)( 83,189)( 84,188)( 85,187)( 86,186)( 87,185)( 88,184)( 89,183)
( 90,182)( 91,181)( 92,180)( 93,179)( 94,178)( 95,177)( 96,176)( 97,175)
( 98,212)( 99,230)(100,229)(101,228)(102,227)(103,226)(104,225)(105,224)
(106,223)(107,222)(108,221)(109,220)(110,219)(111,218)(112,217)(113,216)
(114,215)(115,214)(116,213);
s3 := Sym(230)!(  3,  4)(  5, 21)(  6, 20)(  7, 19)(  8, 18)(  9, 17)( 10, 16)
( 11, 15)( 12, 14)( 22, 23)( 24, 40)( 25, 39)( 26, 38)( 27, 37)( 28, 36)
( 29, 35)( 30, 34)( 31, 33)( 41, 42)( 43, 59)( 44, 58)( 45, 57)( 46, 56)
( 47, 55)( 48, 54)( 49, 53)( 50, 52)( 60, 61)( 62, 78)( 63, 77)( 64, 76)
( 65, 75)( 66, 74)( 67, 73)( 68, 72)( 69, 71)( 79, 80)( 81, 97)( 82, 96)
( 83, 95)( 84, 94)( 85, 93)( 86, 92)( 87, 91)( 88, 90)( 98, 99)(100,116)
(101,115)(102,114)(103,113)(104,112)(105,111)(106,110)(107,109)(117,118)
(119,135)(120,134)(121,133)(122,132)(123,131)(124,130)(125,129)(126,128)
(136,137)(138,154)(139,153)(140,152)(141,151)(142,150)(143,149)(144,148)
(145,147)(155,156)(157,173)(158,172)(159,171)(160,170)(161,169)(162,168)
(163,167)(164,166)(174,175)(176,192)(177,191)(178,190)(179,189)(180,188)
(181,187)(182,186)(183,185)(193,194)(195,211)(196,210)(197,209)(198,208)
(199,207)(200,206)(201,205)(202,204)(212,213)(214,230)(215,229)(216,228)
(217,227)(218,226)(219,225)(220,224)(221,223);
poly := sub<Sym(230)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope