Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,12,4}

Atlas Canonical Name {2,12,4}*768e

Overview

Group
SmallGroup(768,1089367)
Rank
4
Schläfli Type
{2,12,4}
Vertices, edges, …
2, 48, 96, 16
Order of s0s1s2s3
24
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

24-fold

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