Polytope of Type {2,8,12}

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

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

Permutation Representation (Magma) :

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

to this polytope