Polytope of Type {12,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8,2}*768f
if this polytope has a name.
Group : SmallGroup(768,1089120)
Rank : 4
Schlafli Type : {12,8,2}
Number of vertices, edges, etc : 24, 96, 16, 2
Order of s₀s₁s₂s₃ : 12
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 : {12,4,2}*384b, {6,8,2}*384c
   4-fold quotients : {12,4,2}*192b, {12,4,2}*192c, {6,4,2}*192
   8-fold quotients : {12,2,2}*96, {3,4,2}*96, {6,4,2}*96b, {6,4,2}*96c
   16-fold quotients : {3,4,2}*48, {6,2,2}*48
   24-fold quotients : {4,2,2}*32
   32-fold quotients : {3,2,2}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope