Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,12,12}

Atlas Canonical Name {2,12,12}*768b

Overview

Group
SmallGroup(768,1089114)
Rank
4
Schläfli Type
{2,12,12}
Vertices, edges, …
2, 16, 96, 16
Order of s0s1s2s3
8
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

16-fold

48-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (  5,  8)(  6,  7)(  9, 10)( 11, 19)( 12, 20)( 13, 24)( 14, 23)( 15, 22)( 16, 21)( 17, 26)( 18, 25)( 29, 32)( 30, 31)( 33, 34)( 35, 43)( 36, 44)( 37, 48)( 38, 47)( 39, 46)( 40, 45)( 41, 50)( 42, 49)( 51, 52)( 53, 55)( 54, 56)( 59, 68)( 60, 67)( 61, 71)( 62, 72)( 63, 69)( 64, 70)( 65, 73)( 66, 74)( 75, 76)( 77, 79)( 78, 80)( 83, 92)( 84, 91)( 85, 95)( 86, 96)( 87, 93)( 88, 94)( 89, 97)( 90, 98)( 99,123)(100,124)(101,128)(102,127)(103,126)(104,125)(105,130)(106,129)(107,139)(108,140)(109,144)(110,143)(111,142)(112,141)(113,146)(114,145)(115,131)(116,132)(117,136)(118,135)(119,134)(120,133)(121,138)(122,137)(147,172)(148,171)(149,175)(150,176)(151,173)(152,174)(153,177)(154,178)(155,188)(156,187)(157,191)(158,192)(159,189)(160,190)(161,193)(162,194)(163,180)(164,179)(165,183)(166,184)(167,181)(168,182)(169,185)(170,186);;
s2 := (  3,107)(  4,108)(  5,110)(  6,109)(  7,113)(  8,114)(  9,111)( 10,112)( 11, 99)( 12,100)( 13,102)( 14,101)( 15,105)( 16,106)( 17,103)( 18,104)( 19,115)( 20,116)( 21,118)( 22,117)( 23,121)( 24,122)( 25,119)( 26,120)( 27,131)( 28,132)( 29,134)( 30,133)( 31,137)( 32,138)( 33,135)( 34,136)( 35,123)( 36,124)( 37,126)( 38,125)( 39,129)( 40,130)( 41,127)( 42,128)( 43,139)( 44,140)( 45,142)( 46,141)( 47,145)( 48,146)( 49,143)( 50,144)( 51,156)( 52,155)( 53,157)( 54,158)( 55,162)( 56,161)( 57,160)( 58,159)( 59,148)( 60,147)( 61,149)( 62,150)( 63,154)( 64,153)( 65,152)( 66,151)( 67,164)( 68,163)( 69,165)( 70,166)( 71,170)( 72,169)( 73,168)( 74,167)( 75,180)( 76,179)( 77,181)( 78,182)( 79,186)( 80,185)( 81,184)( 82,183)( 83,172)( 84,171)( 85,173)( 86,174)( 87,178)( 88,177)( 89,176)( 90,175)( 91,188)( 92,187)( 93,189)( 94,190)( 95,194)( 96,193)( 97,192)( 98,191);;
s3 := (  3, 57)(  4, 58)(  5, 53)(  6, 54)(  7, 56)(  8, 55)(  9, 51)( 10, 52)( 11, 73)( 12, 74)( 13, 69)( 14, 70)( 15, 72)( 16, 71)( 17, 67)( 18, 68)( 19, 65)( 20, 66)( 21, 61)( 22, 62)( 23, 64)( 24, 63)( 25, 59)( 26, 60)( 27, 81)( 28, 82)( 29, 77)( 30, 78)( 31, 80)( 32, 79)( 33, 75)( 34, 76)( 35, 97)( 36, 98)( 37, 93)( 38, 94)( 39, 96)( 40, 95)( 41, 91)( 42, 92)( 43, 89)( 44, 90)( 45, 85)( 46, 86)( 47, 88)( 48, 87)( 49, 83)( 50, 84)( 99,177)(100,178)(101,173)(102,174)(103,176)(104,175)(105,171)(106,172)(107,193)(108,194)(109,189)(110,190)(111,192)(112,191)(113,187)(114,188)(115,185)(116,186)(117,181)(118,182)(119,184)(120,183)(121,179)(122,180)(123,153)(124,154)(125,149)(126,150)(127,152)(128,151)(129,147)(130,148)(131,169)(132,170)(133,165)(134,166)(135,168)(136,167)(137,163)(138,164)(139,161)(140,162)(141,157)(142,158)(143,160)(144,159)(145,155)(146,156);;
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*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*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)!(  5,  8)(  6,  7)(  9, 10)( 11, 19)( 12, 20)( 13, 24)( 14, 23)( 15, 22)( 16, 21)( 17, 26)( 18, 25)( 29, 32)( 30, 31)( 33, 34)( 35, 43)( 36, 44)( 37, 48)( 38, 47)( 39, 46)( 40, 45)( 41, 50)( 42, 49)( 51, 52)( 53, 55)( 54, 56)( 59, 68)( 60, 67)( 61, 71)( 62, 72)( 63, 69)( 64, 70)( 65, 73)( 66, 74)( 75, 76)( 77, 79)( 78, 80)( 83, 92)( 84, 91)( 85, 95)( 86, 96)( 87, 93)( 88, 94)( 89, 97)( 90, 98)( 99,123)(100,124)(101,128)(102,127)(103,126)(104,125)(105,130)(106,129)(107,139)(108,140)(109,144)(110,143)(111,142)(112,141)(113,146)(114,145)(115,131)(116,132)(117,136)(118,135)(119,134)(120,133)(121,138)(122,137)(147,172)(148,171)(149,175)(150,176)(151,173)(152,174)(153,177)(154,178)(155,188)(156,187)(157,191)(158,192)(159,189)(160,190)(161,193)(162,194)(163,180)(164,179)(165,183)(166,184)(167,181)(168,182)(169,185)(170,186);
s2 := Sym(194)!(  3,107)(  4,108)(  5,110)(  6,109)(  7,113)(  8,114)(  9,111)( 10,112)( 11, 99)( 12,100)( 13,102)( 14,101)( 15,105)( 16,106)( 17,103)( 18,104)( 19,115)( 20,116)( 21,118)( 22,117)( 23,121)( 24,122)( 25,119)( 26,120)( 27,131)( 28,132)( 29,134)( 30,133)( 31,137)( 32,138)( 33,135)( 34,136)( 35,123)( 36,124)( 37,126)( 38,125)( 39,129)( 40,130)( 41,127)( 42,128)( 43,139)( 44,140)( 45,142)( 46,141)( 47,145)( 48,146)( 49,143)( 50,144)( 51,156)( 52,155)( 53,157)( 54,158)( 55,162)( 56,161)( 57,160)( 58,159)( 59,148)( 60,147)( 61,149)( 62,150)( 63,154)( 64,153)( 65,152)( 66,151)( 67,164)( 68,163)( 69,165)( 70,166)( 71,170)( 72,169)( 73,168)( 74,167)( 75,180)( 76,179)( 77,181)( 78,182)( 79,186)( 80,185)( 81,184)( 82,183)( 83,172)( 84,171)( 85,173)( 86,174)( 87,178)( 88,177)( 89,176)( 90,175)( 91,188)( 92,187)( 93,189)( 94,190)( 95,194)( 96,193)( 97,192)( 98,191);
s3 := Sym(194)!(  3, 57)(  4, 58)(  5, 53)(  6, 54)(  7, 56)(  8, 55)(  9, 51)( 10, 52)( 11, 73)( 12, 74)( 13, 69)( 14, 70)( 15, 72)( 16, 71)( 17, 67)( 18, 68)( 19, 65)( 20, 66)( 21, 61)( 22, 62)( 23, 64)( 24, 63)( 25, 59)( 26, 60)( 27, 81)( 28, 82)( 29, 77)( 30, 78)( 31, 80)( 32, 79)( 33, 75)( 34, 76)( 35, 97)( 36, 98)( 37, 93)( 38, 94)( 39, 96)( 40, 95)( 41, 91)( 42, 92)( 43, 89)( 44, 90)( 45, 85)( 46, 86)( 47, 88)( 48, 87)( 49, 83)( 50, 84)( 99,177)(100,178)(101,173)(102,174)(103,176)(104,175)(105,171)(106,172)(107,193)(108,194)(109,189)(110,190)(111,192)(112,191)(113,187)(114,188)(115,185)(116,186)(117,181)(118,182)(119,184)(120,183)(121,179)(122,180)(123,153)(124,154)(125,149)(126,150)(127,152)(128,151)(129,147)(130,148)(131,169)(132,170)(133,165)(134,166)(135,168)(136,167)(137,163)(138,164)(139,161)(140,162)(141,157)(142,158)(143,160)(144,159)(145,155)(146,156);
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*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*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 >;