Polytope of Type {24,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,12}*768e
if this polytope has a name.
Group : SmallGroup(768,1087796)
Rank : 3
Schlafli Type : {24,12}
Number of vertices, edges, etc : 32, 192, 16
Order of s0s1s2 : 8
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,12}*384a
   4-fold quotients : {6,12}*192a, {12,6}*192a
   8-fold quotients : {6,6}*96
   12-fold quotients : {8,4}*64b
   16-fold quotients : {3,6}*48, {6,3}*48
   24-fold quotients : {4,4}*32
   32-fold quotients : {3,3}*24
   48-fold quotients : {2,4}*16, {4,2}*16
   96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   None.

Permutation Representation (GAP) : 
s0 := (  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 15, 16)( 17, 21)( 18, 22)( 19, 24)( 20, 23)( 25, 37)( 26, 38)( 27, 40)( 28, 39)( 29, 45)( 30, 46)( 31, 48)( 32, 47)( 33, 41)( 34, 42)( 35, 44)( 36, 43)( 51, 52)( 53, 57)( 54, 58)( 55, 60)( 56, 59)( 63, 64)( 65, 69)( 66, 70)( 67, 72)( 68, 71)( 73, 85)( 74, 86)( 75, 88)( 76, 87)( 77, 93)( 78, 94)( 79, 96)( 80, 95)( 81, 89)( 82, 90)( 83, 92)( 84, 91)( 97,181)( 98,182)( 99,184)(100,183)(101,189)(102,190)(103,192)(104,191)(105,185)(106,186)(107,188)(108,187)(109,169)(110,170)(111,172)(112,171)(113,177)(114,178)(115,180)(116,179)(117,173)(118,174)(119,176)(120,175)(121,145)(122,146)(123,148)(124,147)(125,153)(126,154)(127,156)(128,155)(129,149)(130,150)(131,152)(132,151)(133,157)(134,158)(135,160)(136,159)(137,165)(138,166)(139,168)(140,167)(141,161)(142,162)(143,164)(144,163);;
s1 := (  1,129)(  2,131)(  3,130)(  4,132)(  5,125)(  6,127)(  7,126)(  8,128)(  9,121)( 10,123)( 11,122)( 12,124)( 13,141)( 14,143)( 15,142)( 16,144)( 17,137)( 18,139)( 19,138)( 20,140)( 21,133)( 22,135)( 23,134)( 24,136)( 25,105)( 26,107)( 27,106)( 28,108)( 29,101)( 30,103)( 31,102)( 32,104)( 33, 97)( 34, 99)( 35, 98)( 36,100)( 37,117)( 38,119)( 39,118)( 40,120)( 41,113)( 42,115)( 43,114)( 44,116)( 45,109)( 46,111)( 47,110)( 48,112)( 49,189)( 50,191)( 51,190)( 52,192)( 53,185)( 54,187)( 55,186)( 56,188)( 57,181)( 58,183)( 59,182)( 60,184)( 61,177)( 62,179)( 63,178)( 64,180)( 65,173)( 66,175)( 67,174)( 68,176)( 69,169)( 70,171)( 71,170)( 72,172)( 73,165)( 74,167)( 75,166)( 76,168)( 77,161)( 78,163)( 79,162)( 80,164)( 81,157)( 82,159)( 83,158)( 84,160)( 85,153)( 86,155)( 87,154)( 88,156)( 89,149)( 90,151)( 91,150)( 92,152)( 93,145)( 94,147)( 95,146)( 96,148);;
s2 := (  1,  2)(  5, 10)(  6,  9)(  7, 11)(  8, 12)( 13, 14)( 17, 22)( 18, 21)( 19, 23)( 20, 24)( 25, 26)( 29, 34)( 30, 33)( 31, 35)( 32, 36)( 37, 38)( 41, 46)( 42, 45)( 43, 47)( 44, 48)( 49, 62)( 50, 61)( 51, 63)( 52, 64)( 53, 70)( 54, 69)( 55, 71)( 56, 72)( 57, 66)( 58, 65)( 59, 67)( 60, 68)( 73, 86)( 74, 85)( 75, 87)( 76, 88)( 77, 94)( 78, 93)( 79, 95)( 80, 96)( 81, 90)( 82, 89)( 83, 91)( 84, 92)( 97,122)( 98,121)( 99,123)(100,124)(101,130)(102,129)(103,131)(104,132)(105,126)(106,125)(107,127)(108,128)(109,134)(110,133)(111,135)(112,136)(113,142)(114,141)(115,143)(116,144)(117,138)(118,137)(119,139)(120,140)(145,182)(146,181)(147,183)(148,184)(149,190)(150,189)(151,191)(152,192)(153,186)(154,185)(155,187)(156,188)(157,170)(158,169)(159,171)(160,172)(161,178)(162,177)(163,179)(164,180)(165,174)(166,173)(167,175)(168,176);;
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, s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(192)!(  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 15, 16)( 17, 21)( 18, 22)( 19, 24)( 20, 23)( 25, 37)( 26, 38)( 27, 40)( 28, 39)( 29, 45)( 30, 46)( 31, 48)( 32, 47)( 33, 41)( 34, 42)( 35, 44)( 36, 43)( 51, 52)( 53, 57)( 54, 58)( 55, 60)( 56, 59)( 63, 64)( 65, 69)( 66, 70)( 67, 72)( 68, 71)( 73, 85)( 74, 86)( 75, 88)( 76, 87)( 77, 93)( 78, 94)( 79, 96)( 80, 95)( 81, 89)( 82, 90)( 83, 92)( 84, 91)( 97,181)( 98,182)( 99,184)(100,183)(101,189)(102,190)(103,192)(104,191)(105,185)(106,186)(107,188)(108,187)(109,169)(110,170)(111,172)(112,171)(113,177)(114,178)(115,180)(116,179)(117,173)(118,174)(119,176)(120,175)(121,145)(122,146)(123,148)(124,147)(125,153)(126,154)(127,156)(128,155)(129,149)(130,150)(131,152)(132,151)(133,157)(134,158)(135,160)(136,159)(137,165)(138,166)(139,168)(140,167)(141,161)(142,162)(143,164)(144,163);
s1 := Sym(192)!(  1,129)(  2,131)(  3,130)(  4,132)(  5,125)(  6,127)(  7,126)(  8,128)(  9,121)( 10,123)( 11,122)( 12,124)( 13,141)( 14,143)( 15,142)( 16,144)( 17,137)( 18,139)( 19,138)( 20,140)( 21,133)( 22,135)( 23,134)( 24,136)( 25,105)( 26,107)( 27,106)( 28,108)( 29,101)( 30,103)( 31,102)( 32,104)( 33, 97)( 34, 99)( 35, 98)( 36,100)( 37,117)( 38,119)( 39,118)( 40,120)( 41,113)( 42,115)( 43,114)( 44,116)( 45,109)( 46,111)( 47,110)( 48,112)( 49,189)( 50,191)( 51,190)( 52,192)( 53,185)( 54,187)( 55,186)( 56,188)( 57,181)( 58,183)( 59,182)( 60,184)( 61,177)( 62,179)( 63,178)( 64,180)( 65,173)( 66,175)( 67,174)( 68,176)( 69,169)( 70,171)( 71,170)( 72,172)( 73,165)( 74,167)( 75,166)( 76,168)( 77,161)( 78,163)( 79,162)( 80,164)( 81,157)( 82,159)( 83,158)( 84,160)( 85,153)( 86,155)( 87,154)( 88,156)( 89,149)( 90,151)( 91,150)( 92,152)( 93,145)( 94,147)( 95,146)( 96,148);
s2 := Sym(192)!(  1,  2)(  5, 10)(  6,  9)(  7, 11)(  8, 12)( 13, 14)( 17, 22)( 18, 21)( 19, 23)( 20, 24)( 25, 26)( 29, 34)( 30, 33)( 31, 35)( 32, 36)( 37, 38)( 41, 46)( 42, 45)( 43, 47)( 44, 48)( 49, 62)( 50, 61)( 51, 63)( 52, 64)( 53, 70)( 54, 69)( 55, 71)( 56, 72)( 57, 66)( 58, 65)( 59, 67)( 60, 68)( 73, 86)( 74, 85)( 75, 87)( 76, 88)( 77, 94)( 78, 93)( 79, 95)( 80, 96)( 81, 90)( 82, 89)( 83, 91)( 84, 92)( 97,122)( 98,121)( 99,123)(100,124)(101,130)(102,129)(103,131)(104,132)(105,126)(106,125)(107,127)(108,128)(109,134)(110,133)(111,135)(112,136)(113,142)(114,141)(115,143)(116,144)(117,138)(118,137)(119,139)(120,140)(145,182)(146,181)(147,183)(148,184)(149,190)(150,189)(151,191)(152,192)(153,186)(154,185)(155,187)(156,188)(157,170)(158,169)(159,171)(160,172)(161,178)(162,177)(163,179)(164,180)(165,174)(166,173)(167,175)(168,176);
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, s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1 >;
References : None.
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