Polytope of Type {2,12,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,4}*768e
if this polytope has a name.
Group : SmallGroup(768,1089367)
Rank : 4
Schlafli Type : {2,12,4}
Number of vertices, edges, etc : 2, 48, 96, 16
Order of s₀s₁s₂s₃ : 24
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 : {2,6,4}*384b
   4-fold quotients : {2,6,4}*192
   8-fold quotients : {2,6,4}*96a, {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
   16-fold quotients : {2,3,4}*48, {2,6,2}*48
   24-fold quotients : {2,2,4}*32
   32-fold quotients : {2,3,2}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope