Polytope of Type {2,16,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,16,12}*768a
if this polytope has a name.
Group : SmallGroup(768,323305)
Rank : 4
Schlafli Type : {2,16,12}
Number of vertices, edges, etc : 2, 16, 96, 12
Order of s₀s₁s₂s₃ : 48
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 : {2,8,12}*384a, {2,16,6}*384
   3-fold quotients : {2,16,4}*256a
   4-fold quotients : {2,4,12}*192a, {2,8,6}*192
   6-fold quotients : {2,8,4}*128a, {2,16,2}*128
   8-fold quotients : {2,2,12}*96, {2,4,6}*96a
   12-fold quotients : {2,4,4}*64, {2,8,2}*64
   16-fold quotients : {2,2,6}*48
   24-fold quotients : {2,2,4}*32, {2,4,2}*32
   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, 99)(  4,100)(  5,101)(  6,102)(  7,103)(  8,104)(  9,108)( 10,109)( 11,110)( 12,105)( 13,106)( 14,107)( 15,111)( 16,112)( 17,113)( 18,114)( 19,115)( 20,116)( 21,120)( 22,121)( 23,122)( 24,117)( 25,118)( 26,119)( 27,129)( 28,130)( 29,131)( 30,132)( 31,133)( 32,134)( 33,123)( 34,124)( 35,125)( 36,126)( 37,127)( 38,128)( 39,141)( 40,142)( 41,143)( 42,144)( 43,145)( 44,146)( 45,135)( 46,136)( 47,137)( 48,138)( 49,139)( 50,140)( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)( 56,152)( 57,156)( 58,157)( 59,158)( 60,153)( 61,154)( 62,155)( 63,159)( 64,160)( 65,161)( 66,162)( 67,163)( 68,164)( 69,168)( 70,169)( 71,170)( 72,165)( 73,166)( 74,167)( 75,177)( 76,178)( 77,179)( 78,180)( 79,181)( 80,182)( 81,171)( 82,172)( 83,173)( 84,174)( 85,175)( 86,176)( 87,189)( 88,190)( 89,191)( 90,192)( 91,193)( 92,194)( 93,183)( 94,184)( 95,185)( 96,186)( 97,187)( 98,188);;
s2 := (  4,  5)(  7,  8)(  9, 12)( 10, 14)( 11, 13)( 16, 17)( 19, 20)( 21, 24)( 22, 26)( 23, 25)( 27, 33)( 28, 35)( 29, 34)( 30, 36)( 31, 38)( 32, 37)( 39, 45)( 40, 47)( 41, 46)( 42, 48)( 43, 50)( 44, 49)( 51, 63)( 52, 65)( 53, 64)( 54, 66)( 55, 68)( 56, 67)( 57, 72)( 58, 74)( 59, 73)( 60, 69)( 61, 71)( 62, 70)( 75, 93)( 76, 95)( 77, 94)( 78, 96)( 79, 98)( 80, 97)( 81, 87)( 82, 89)( 83, 88)( 84, 90)( 85, 92)( 86, 91)( 99,123)(100,125)(101,124)(102,126)(103,128)(104,127)(105,132)(106,134)(107,133)(108,129)(109,131)(110,130)(111,135)(112,137)(113,136)(114,138)(115,140)(116,139)(117,144)(118,146)(119,145)(120,141)(121,143)(122,142)(147,183)(148,185)(149,184)(150,186)(151,188)(152,187)(153,192)(154,194)(155,193)(156,189)(157,191)(158,190)(159,171)(160,173)(161,172)(162,174)(163,176)(164,175)(165,180)(166,182)(167,181)(168,177)(169,179)(170,178);;
s3 := (  3, 52)(  4, 51)(  5, 53)(  6, 55)(  7, 54)(  8, 56)(  9, 58)( 10, 57)( 11, 59)( 12, 61)( 13, 60)( 14, 62)( 15, 64)( 16, 63)( 17, 65)( 18, 67)( 19, 66)( 20, 68)( 21, 70)( 22, 69)( 23, 71)( 24, 73)( 25, 72)( 26, 74)( 27, 76)( 28, 75)( 29, 77)( 30, 79)( 31, 78)( 32, 80)( 33, 82)( 34, 81)( 35, 83)( 36, 85)( 37, 84)( 38, 86)( 39, 88)( 40, 87)( 41, 89)( 42, 91)( 43, 90)( 44, 92)( 45, 94)( 46, 93)( 47, 95)( 48, 97)( 49, 96)( 50, 98)( 99,148)(100,147)(101,149)(102,151)(103,150)(104,152)(105,154)(106,153)(107,155)(108,157)(109,156)(110,158)(111,160)(112,159)(113,161)(114,163)(115,162)(116,164)(117,166)(118,165)(119,167)(120,169)(121,168)(122,170)(123,172)(124,171)(125,173)(126,175)(127,174)(128,176)(129,178)(130,177)(131,179)(132,181)(133,180)(134,182)(135,184)(136,183)(137,185)(138,187)(139,186)(140,188)(141,190)(142,189)(143,191)(144,193)(145,192)(146,194);;
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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(194)!(1,2);
s1 := Sym(194)!(  3, 99)(  4,100)(  5,101)(  6,102)(  7,103)(  8,104)(  9,108)( 10,109)( 11,110)( 12,105)( 13,106)( 14,107)( 15,111)( 16,112)( 17,113)( 18,114)( 19,115)( 20,116)( 21,120)( 22,121)( 23,122)( 24,117)( 25,118)( 26,119)( 27,129)( 28,130)( 29,131)( 30,132)( 31,133)( 32,134)( 33,123)( 34,124)( 35,125)( 36,126)( 37,127)( 38,128)( 39,141)( 40,142)( 41,143)( 42,144)( 43,145)( 44,146)( 45,135)( 46,136)( 47,137)( 48,138)( 49,139)( 50,140)( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)( 56,152)( 57,156)( 58,157)( 59,158)( 60,153)( 61,154)( 62,155)( 63,159)( 64,160)( 65,161)( 66,162)( 67,163)( 68,164)( 69,168)( 70,169)( 71,170)( 72,165)( 73,166)( 74,167)( 75,177)( 76,178)( 77,179)( 78,180)( 79,181)( 80,182)( 81,171)( 82,172)( 83,173)( 84,174)( 85,175)( 86,176)( 87,189)( 88,190)( 89,191)( 90,192)( 91,193)( 92,194)( 93,183)( 94,184)( 95,185)( 96,186)( 97,187)( 98,188);
s2 := Sym(194)!(  4,  5)(  7,  8)(  9, 12)( 10, 14)( 11, 13)( 16, 17)( 19, 20)( 21, 24)( 22, 26)( 23, 25)( 27, 33)( 28, 35)( 29, 34)( 30, 36)( 31, 38)( 32, 37)( 39, 45)( 40, 47)( 41, 46)( 42, 48)( 43, 50)( 44, 49)( 51, 63)( 52, 65)( 53, 64)( 54, 66)( 55, 68)( 56, 67)( 57, 72)( 58, 74)( 59, 73)( 60, 69)( 61, 71)( 62, 70)( 75, 93)( 76, 95)( 77, 94)( 78, 96)( 79, 98)( 80, 97)( 81, 87)( 82, 89)( 83, 88)( 84, 90)( 85, 92)( 86, 91)( 99,123)(100,125)(101,124)(102,126)(103,128)(104,127)(105,132)(106,134)(107,133)(108,129)(109,131)(110,130)(111,135)(112,137)(113,136)(114,138)(115,140)(116,139)(117,144)(118,146)(119,145)(120,141)(121,143)(122,142)(147,183)(148,185)(149,184)(150,186)(151,188)(152,187)(153,192)(154,194)(155,193)(156,189)(157,191)(158,190)(159,171)(160,173)(161,172)(162,174)(163,176)(164,175)(165,180)(166,182)(167,181)(168,177)(169,179)(170,178);
s3 := Sym(194)!(  3, 52)(  4, 51)(  5, 53)(  6, 55)(  7, 54)(  8, 56)(  9, 58)( 10, 57)( 11, 59)( 12, 61)( 13, 60)( 14, 62)( 15, 64)( 16, 63)( 17, 65)( 18, 67)( 19, 66)( 20, 68)( 21, 70)( 22, 69)( 23, 71)( 24, 73)( 25, 72)( 26, 74)( 27, 76)( 28, 75)( 29, 77)( 30, 79)( 31, 78)( 32, 80)( 33, 82)( 34, 81)( 35, 83)( 36, 85)( 37, 84)( 38, 86)( 39, 88)( 40, 87)( 41, 89)( 42, 91)( 43, 90)( 44, 92)( 45, 94)( 46, 93)( 47, 95)( 48, 97)( 49, 96)( 50, 98)( 99,148)(100,147)(101,149)(102,151)(103,150)(104,152)(105,154)(106,153)(107,155)(108,157)(109,156)(110,158)(111,160)(112,159)(113,161)(114,163)(115,162)(116,164)(117,166)(118,165)(119,167)(120,169)(121,168)(122,170)(123,172)(124,171)(125,173)(126,175)(127,174)(128,176)(129,178)(130,177)(131,179)(132,181)(133,180)(134,182)(135,184)(136,183)(137,185)(138,187)(139,186)(140,188)(141,190)(142,189)(143,191)(144,193)(145,192)(146,194);
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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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 >;

to this polytope