Polytope of Type {8,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12}*384a
if this polytope has a name.
Group : SmallGroup(384,860)
Rank : 3
Schlafli Type : {8,12}
Number of vertices, edges, etc : 16, 96, 24
Order of s0s1s2 : 24
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,12,2} of size 768
Vertex Figure Of :
   {2,8,12} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,12}*192a, {8,12}*192a, {8,12}*192b
   3-fold quotients : {8,4}*128a
   4-fold quotients : {4,12}*96a, {8,6}*96
   6-fold quotients : {8,4}*64a, {8,4}*64b, {4,4}*64
   8-fold quotients : {2,12}*48, {4,6}*48a
   12-fold quotients : {4,4}*32, {8,2}*32
   16-fold quotients : {2,6}*24
   24-fold quotients : {2,4}*16, {4,2}*16
   32-fold quotients : {2,3}*12
   48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,24}*768a, {8,12}*768a, {8,24}*768c, {16,12}*768a, {16,12}*768b
   3-fold covers : {8,36}*1152a, {24,12}*1152b, {24,12}*1152c
   5-fold covers : {8,60}*1920a, {40,12}*1920a
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 2.
      12 facets:
         12 of {8}*16
      12 vertex figures:
         8 of {6}*12
         4 of {12}*24

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