Polytope of Type {2,12,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,12}*768d
if this polytope has a name.
Group : SmallGroup(768,1089263)
Rank : 4
Schlafli Type : {2,12,12}
Number of vertices, edges, etc : 2, 16, 96, 16
Order of s₀s₁s₂s₃ : 8
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 : {2,12,6}*384a, {2,6,12}*384b
   4-fold quotients : {2,3,12}*192, {2,6,6}*192
   8-fold quotients : {2,3,6}*96, {2,6,3}*96
   16-fold quotients : {2,3,3}*48
   24-fold quotients : {2,4,2}*32
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope