Polytope of Type {12,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4,2}*768c
if this polytope has a name.
Group : SmallGroup(768,1087527)
Rank : 4
Schlafli Type : {12,4,2}
Number of vertices, edges, etc : 48, 96, 16, 2
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   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) :
   2-fold quotients : {6,4,2}*384a
   4-fold quotients : {12,4,2}*192c
   8-fold quotients : {6,4,2}*96c
   16-fold quotients : {3,4,2}*48
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, 33)( 18, 34)
( 19, 36)( 20, 35)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 37)( 26, 38)
( 27, 40)( 28, 39)( 29, 45)( 30, 46)( 31, 48)( 32, 47)( 51, 52)( 53, 57)
( 54, 58)( 55, 60)( 56, 59)( 63, 64)( 65, 81)( 66, 82)( 67, 84)( 68, 83)
( 69, 89)( 70, 90)( 71, 92)( 72, 91)( 73, 85)( 74, 86)( 75, 88)( 76, 87)
( 77, 93)( 78, 94)( 79, 96)( 80, 95)( 97,145)( 98,146)( 99,148)(100,147)
(101,153)(102,154)(103,156)(104,155)(105,149)(106,150)(107,152)(108,151)
(109,157)(110,158)(111,160)(112,159)(113,177)(114,178)(115,180)(116,179)
(117,185)(118,186)(119,188)(120,187)(121,181)(122,182)(123,184)(124,183)
(125,189)(126,190)(127,192)(128,191)(129,161)(130,162)(131,164)(132,163)
(133,169)(134,170)(135,172)(136,171)(137,165)(138,166)(139,168)(140,167)
(141,173)(142,174)(143,176)(144,175);;
s1 := (  1,113)(  2,116)(  3,115)(  4,114)(  5,119)(  6,118)(  7,117)(  8,120)
(  9,126)( 10,127)( 11,128)( 12,125)( 13,124)( 14,121)( 15,122)( 16,123)
( 17, 97)( 18,100)( 19, 99)( 20, 98)( 21,103)( 22,102)( 23,101)( 24,104)
( 25,110)( 26,111)( 27,112)( 28,109)( 29,108)( 30,105)( 31,106)( 32,107)
( 33,129)( 34,132)( 35,131)( 36,130)( 37,135)( 38,134)( 39,133)( 40,136)
( 41,142)( 42,143)( 43,144)( 44,141)( 45,140)( 46,137)( 47,138)( 48,139)
( 49,161)( 50,164)( 51,163)( 52,162)( 53,167)( 54,166)( 55,165)( 56,168)
( 57,174)( 58,175)( 59,176)( 60,173)( 61,172)( 62,169)( 63,170)( 64,171)
( 65,145)( 66,148)( 67,147)( 68,146)( 69,151)( 70,150)( 71,149)( 72,152)
( 73,158)( 74,159)( 75,160)( 76,157)( 77,156)( 78,153)( 79,154)( 80,155)
( 81,177)( 82,180)( 83,179)( 84,178)( 85,183)( 86,182)( 87,181)( 88,184)
( 89,190)( 90,191)( 91,192)( 92,189)( 93,188)( 94,185)( 95,186)( 96,187);;
s2 := (  1, 61)(  2, 62)(  3, 63)(  4, 64)(  5, 57)(  6, 58)(  7, 59)(  8, 60)
(  9, 53)( 10, 54)( 11, 55)( 12, 56)( 13, 49)( 14, 50)( 15, 51)( 16, 52)
( 17, 77)( 18, 78)( 19, 79)( 20, 80)( 21, 73)( 22, 74)( 23, 75)( 24, 76)
( 25, 69)( 26, 70)( 27, 71)( 28, 72)( 29, 65)( 30, 66)( 31, 67)( 32, 68)
( 33, 93)( 34, 94)( 35, 95)( 36, 96)( 37, 89)( 38, 90)( 39, 91)( 40, 92)
( 41, 85)( 42, 86)( 43, 87)( 44, 88)( 45, 81)( 46, 82)( 47, 83)( 48, 84)
( 97,157)( 98,158)( 99,159)(100,160)(101,153)(102,154)(103,155)(104,156)
(105,149)(106,150)(107,151)(108,152)(109,145)(110,146)(111,147)(112,148)
(113,173)(114,174)(115,175)(116,176)(117,169)(118,170)(119,171)(120,172)
(121,165)(122,166)(123,167)(124,168)(125,161)(126,162)(127,163)(128,164)
(129,189)(130,190)(131,191)(132,192)(133,185)(134,186)(135,187)(136,188)
(137,181)(138,182)(139,183)(140,184)(141,177)(142,178)(143,179)(144,180);;
s3 := (193,194);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope