Polytope of Type {2,38,12}

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

s0 := (1,2);;
s1 := (  4, 21)(  5, 20)(  6, 19)(  7, 18)(  8, 17)(  9, 16)( 10, 15)( 11, 14)
( 12, 13)( 23, 40)( 24, 39)( 25, 38)( 26, 37)( 27, 36)( 28, 35)( 29, 34)
( 30, 33)( 31, 32)( 42, 59)( 43, 58)( 44, 57)( 45, 56)( 46, 55)( 47, 54)
( 48, 53)( 49, 52)( 50, 51)( 61, 78)( 62, 77)( 63, 76)( 64, 75)( 65, 74)
( 66, 73)( 67, 72)( 68, 71)( 69, 70)( 80, 97)( 81, 96)( 82, 95)( 83, 94)
( 84, 93)( 85, 92)( 86, 91)( 87, 90)( 88, 89)( 99,116)(100,115)(101,114)
(102,113)(103,112)(104,111)(105,110)(106,109)(107,108)(118,135)(119,134)
(120,133)(121,132)(122,131)(123,130)(124,129)(125,128)(126,127)(137,154)
(138,153)(139,152)(140,151)(141,150)(142,149)(143,148)(144,147)(145,146)
(156,173)(157,172)(158,171)(159,170)(160,169)(161,168)(162,167)(163,166)
(164,165)(175,192)(176,191)(177,190)(178,189)(179,188)(180,187)(181,186)
(182,185)(183,184)(194,211)(195,210)(196,209)(197,208)(198,207)(199,206)
(200,205)(201,204)(202,203)(213,230)(214,229)(215,228)(216,227)(217,226)
(218,225)(219,224)(220,223)(221,222);;
s2 := (  3,  4)(  5, 21)(  6, 20)(  7, 19)(  8, 18)(  9, 17)( 10, 16)( 11, 15)
( 12, 14)( 22, 42)( 23, 41)( 24, 59)( 25, 58)( 26, 57)( 27, 56)( 28, 55)
( 29, 54)( 30, 53)( 31, 52)( 32, 51)( 33, 50)( 34, 49)( 35, 48)( 36, 47)
( 37, 46)( 38, 45)( 39, 44)( 40, 43)( 60, 61)( 62, 78)( 63, 77)( 64, 76)
( 65, 75)( 66, 74)( 67, 73)( 68, 72)( 69, 71)( 79, 99)( 80, 98)( 81,116)
( 82,115)( 83,114)( 84,113)( 85,112)( 86,111)( 87,110)( 88,109)( 89,108)
( 90,107)( 91,106)( 92,105)( 93,104)( 94,103)( 95,102)( 96,101)( 97,100)
(117,175)(118,174)(119,192)(120,191)(121,190)(122,189)(123,188)(124,187)
(125,186)(126,185)(127,184)(128,183)(129,182)(130,181)(131,180)(132,179)
(133,178)(134,177)(135,176)(136,213)(137,212)(138,230)(139,229)(140,228)
(141,227)(142,226)(143,225)(144,224)(145,223)(146,222)(147,221)(148,220)
(149,219)(150,218)(151,217)(152,216)(153,215)(154,214)(155,194)(156,193)
(157,211)(158,210)(159,209)(160,208)(161,207)(162,206)(163,205)(164,204)
(165,203)(166,202)(167,201)(168,200)(169,199)(170,198)(171,197)(172,196)
(173,195);;
s3 := (  3,136)(  4,137)(  5,138)(  6,139)(  7,140)(  8,141)(  9,142)( 10,143)
( 11,144)( 12,145)( 13,146)( 14,147)( 15,148)( 16,149)( 17,150)( 18,151)
( 19,152)( 20,153)( 21,154)( 22,117)( 23,118)( 24,119)( 25,120)( 26,121)
( 27,122)( 28,123)( 29,124)( 30,125)( 31,126)( 32,127)( 33,128)( 34,129)
( 35,130)( 36,131)( 37,132)( 38,133)( 39,134)( 40,135)( 41,155)( 42,156)
( 43,157)( 44,158)( 45,159)( 46,160)( 47,161)( 48,162)( 49,163)( 50,164)
( 51,165)( 52,166)( 53,167)( 54,168)( 55,169)( 56,170)( 57,171)( 58,172)
( 59,173)( 60,193)( 61,194)( 62,195)( 63,196)( 64,197)( 65,198)( 66,199)
( 67,200)( 68,201)( 69,202)( 70,203)( 71,204)( 72,205)( 73,206)( 74,207)
( 75,208)( 76,209)( 77,210)( 78,211)( 79,174)( 80,175)( 81,176)( 82,177)
( 83,178)( 84,179)( 85,180)( 86,181)( 87,182)( 88,183)( 89,184)( 90,185)
( 91,186)( 92,187)( 93,188)( 94,189)( 95,190)( 96,191)( 97,192)( 98,212)
( 99,213)(100,214)(101,215)(102,216)(103,217)(104,218)(105,219)(106,220)
(107,221)(108,222)(109,223)(110,224)(111,225)(112,226)(113,227)(114,228)
(115,229)(116,230);;
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(230)!(1,2);
s1 := Sym(230)!(  4, 21)(  5, 20)(  6, 19)(  7, 18)(  8, 17)(  9, 16)( 10, 15)
( 11, 14)( 12, 13)( 23, 40)( 24, 39)( 25, 38)( 26, 37)( 27, 36)( 28, 35)
( 29, 34)( 30, 33)( 31, 32)( 42, 59)( 43, 58)( 44, 57)( 45, 56)( 46, 55)
( 47, 54)( 48, 53)( 49, 52)( 50, 51)( 61, 78)( 62, 77)( 63, 76)( 64, 75)
( 65, 74)( 66, 73)( 67, 72)( 68, 71)( 69, 70)( 80, 97)( 81, 96)( 82, 95)
( 83, 94)( 84, 93)( 85, 92)( 86, 91)( 87, 90)( 88, 89)( 99,116)(100,115)
(101,114)(102,113)(103,112)(104,111)(105,110)(106,109)(107,108)(118,135)
(119,134)(120,133)(121,132)(122,131)(123,130)(124,129)(125,128)(126,127)
(137,154)(138,153)(139,152)(140,151)(141,150)(142,149)(143,148)(144,147)
(145,146)(156,173)(157,172)(158,171)(159,170)(160,169)(161,168)(162,167)
(163,166)(164,165)(175,192)(176,191)(177,190)(178,189)(179,188)(180,187)
(181,186)(182,185)(183,184)(194,211)(195,210)(196,209)(197,208)(198,207)
(199,206)(200,205)(201,204)(202,203)(213,230)(214,229)(215,228)(216,227)
(217,226)(218,225)(219,224)(220,223)(221,222);
s2 := Sym(230)!(  3,  4)(  5, 21)(  6, 20)(  7, 19)(  8, 18)(  9, 17)( 10, 16)
( 11, 15)( 12, 14)( 22, 42)( 23, 41)( 24, 59)( 25, 58)( 26, 57)( 27, 56)
( 28, 55)( 29, 54)( 30, 53)( 31, 52)( 32, 51)( 33, 50)( 34, 49)( 35, 48)
( 36, 47)( 37, 46)( 38, 45)( 39, 44)( 40, 43)( 60, 61)( 62, 78)( 63, 77)
( 64, 76)( 65, 75)( 66, 74)( 67, 73)( 68, 72)( 69, 71)( 79, 99)( 80, 98)
( 81,116)( 82,115)( 83,114)( 84,113)( 85,112)( 86,111)( 87,110)( 88,109)
( 89,108)( 90,107)( 91,106)( 92,105)( 93,104)( 94,103)( 95,102)( 96,101)
( 97,100)(117,175)(118,174)(119,192)(120,191)(121,190)(122,189)(123,188)
(124,187)(125,186)(126,185)(127,184)(128,183)(129,182)(130,181)(131,180)
(132,179)(133,178)(134,177)(135,176)(136,213)(137,212)(138,230)(139,229)
(140,228)(141,227)(142,226)(143,225)(144,224)(145,223)(146,222)(147,221)
(148,220)(149,219)(150,218)(151,217)(152,216)(153,215)(154,214)(155,194)
(156,193)(157,211)(158,210)(159,209)(160,208)(161,207)(162,206)(163,205)
(164,204)(165,203)(166,202)(167,201)(168,200)(169,199)(170,198)(171,197)
(172,196)(173,195);
s3 := Sym(230)!(  3,136)(  4,137)(  5,138)(  6,139)(  7,140)(  8,141)(  9,142)
( 10,143)( 11,144)( 12,145)( 13,146)( 14,147)( 15,148)( 16,149)( 17,150)
( 18,151)( 19,152)( 20,153)( 21,154)( 22,117)( 23,118)( 24,119)( 25,120)
( 26,121)( 27,122)( 28,123)( 29,124)( 30,125)( 31,126)( 32,127)( 33,128)
( 34,129)( 35,130)( 36,131)( 37,132)( 38,133)( 39,134)( 40,135)( 41,155)
( 42,156)( 43,157)( 44,158)( 45,159)( 46,160)( 47,161)( 48,162)( 49,163)
( 50,164)( 51,165)( 52,166)( 53,167)( 54,168)( 55,169)( 56,170)( 57,171)
( 58,172)( 59,173)( 60,193)( 61,194)( 62,195)( 63,196)( 64,197)( 65,198)
( 66,199)( 67,200)( 68,201)( 69,202)( 70,203)( 71,204)( 72,205)( 73,206)
( 74,207)( 75,208)( 76,209)( 77,210)( 78,211)( 79,174)( 80,175)( 81,176)
( 82,177)( 83,178)( 84,179)( 85,180)( 86,181)( 87,182)( 88,183)( 89,184)
( 90,185)( 91,186)( 92,187)( 93,188)( 94,189)( 95,190)( 96,191)( 97,192)
( 98,212)( 99,213)(100,214)(101,215)(102,216)(103,217)(104,218)(105,219)
(106,220)(107,221)(108,222)(109,223)(110,224)(111,225)(112,226)(113,227)
(114,228)(115,229)(116,230);
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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