Polytope of Type {4,12,2}

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

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