Polytope of Type {12,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,16}*384a
Also Known As : {12,16|2}. if this polytope has another name.
Group : SmallGroup(384,1767)
Rank : 3
Schlafli Type : {12,16}
Number of vertices, edges, etc : 12, 96, 16
Order of s₀s₁s₂ : 48
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {12,16,2} of size 768
Vertex Figure Of :
   {2,12,16} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,8}*192a, {6,16}*192
   3-fold quotients : {4,16}*128a
   4-fold quotients : {12,4}*96a, {6,8}*96
   6-fold quotients : {4,8}*64a, {2,16}*64
   8-fold quotients : {12,2}*48, {6,4}*48a
   12-fold quotients : {4,4}*32, {2,8}*32
   16-fold quotients : {6,2}*24
   24-fold quotients : {2,4}*16, {4,2}*16
   32-fold quotients : {3,2}*12
   48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,16}*768a, {24,16}*768c, {24,16}*768d, {12,32}*768a, {12,32}*768b
   3-fold covers : {36,16}*1152a, {12,48}*1152b, {12,48}*1152c
   5-fold covers : {60,16}*1920a, {12,80}*1920a
Permutation Representation (GAP) :

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