Polytope of Type {12,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8}*384h
if this polytope has a name.
Group : SmallGroup(384,17986)
Rank : 3
Schlafli Type : {12,8}
Number of vertices, edges, etc : 24, 96, 16
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {12,8,2} of size 768
Vertex Figure Of :
   {2,12,8} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,4}*192c, {6,8}*192b
   4-fold quotients : {3,8}*96, {6,4}*96
   8-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
   16-fold quotients : {3,4}*24, {6,2}*24
   32-fold quotients : {3,2}*12
   48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {24,8}*768n, {24,8}*768p, {12,8}*768s
   3-fold covers : {36,8}*1152h, {12,24}*1152m, {12,24}*1152v
   5-fold covers : {12,40}*1920h, {60,8}*1920h
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 := (  1,153)(  2,154)(  3,156)(  4,155)(  5,159)(  6,160)(  7,157)(  8,158)
(  9,145)( 10,146)( 11,148)( 12,147)( 13,151)( 14,152)( 15,149)( 16,150)
( 17,161)( 18,162)( 19,164)( 20,163)( 21,167)( 22,168)( 23,165)( 24,166)
( 25,177)( 26,178)( 27,180)( 28,179)( 29,183)( 30,184)( 31,181)( 32,182)
( 33,169)( 34,170)( 35,172)( 36,171)( 37,175)( 38,176)( 39,173)( 40,174)
( 41,185)( 42,186)( 43,188)( 44,187)( 45,191)( 46,192)( 47,189)( 48,190)
( 49,129)( 50,130)( 51,132)( 52,131)( 53,135)( 54,136)( 55,133)( 56,134)
( 57,121)( 58,122)( 59,124)( 60,123)( 61,127)( 62,128)( 63,125)( 64,126)
( 65,137)( 66,138)( 67,140)( 68,139)( 69,143)( 70,144)( 71,141)( 72,142)
( 73,105)( 74,106)( 75,108)( 76,107)( 77,111)( 78,112)( 79,109)( 80,110)
( 81, 97)( 82, 98)( 83,100)( 84, 99)( 85,103)( 86,104)( 87,101)( 88,102)
( 89,113)( 90,114)( 91,116)( 92,115)( 93,119)( 94,120)( 95,117)( 96,118);;
s2 := (  1, 55)(  2, 56)(  3, 53)(  4, 54)(  5, 52)(  6, 51)(  7, 50)(  8, 49)
(  9, 63)( 10, 64)( 11, 61)( 12, 62)( 13, 60)( 14, 59)( 15, 58)( 16, 57)
( 17, 71)( 18, 72)( 19, 69)( 20, 70)( 21, 68)( 22, 67)( 23, 66)( 24, 65)
( 25, 79)( 26, 80)( 27, 77)( 28, 78)( 29, 76)( 30, 75)( 31, 74)( 32, 73)
( 33, 87)( 34, 88)( 35, 85)( 36, 86)( 37, 84)( 38, 83)( 39, 82)( 40, 81)
( 41, 95)( 42, 96)( 43, 93)( 44, 94)( 45, 92)( 46, 91)( 47, 90)( 48, 89)
( 97,151)( 98,152)( 99,149)(100,150)(101,148)(102,147)(103,146)(104,145)
(105,159)(106,160)(107,157)(108,158)(109,156)(110,155)(111,154)(112,153)
(113,167)(114,168)(115,165)(116,166)(117,164)(118,163)(119,162)(120,161)
(121,175)(122,176)(123,173)(124,174)(125,172)(126,171)(127,170)(128,169)
(129,183)(130,184)(131,181)(132,182)(133,180)(134,179)(135,178)(136,177)
(137,191)(138,192)(139,189)(140,190)(141,188)(142,187)(143,186)(144,185);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s2 >;

References : None.
to this polytope