Polytope of Type {2,4,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,12}*768c
if this polytope has a name.
Group : SmallGroup(768,1087527)
Rank : 4
Schlafli Type : {2,4,12}
Number of vertices, edges, etc : 2, 16, 96, 48
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 : {2,4,6}*384a
   4-fold quotients : {2,4,12}*192c
   8-fold quotients : {2,4,6}*96c
   16-fold quotients : {2,4,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope