Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,6,4,2}

Atlas Canonical Name {4,6,4,2}*768c

Overview

Group
SmallGroup(768,1090234)
Rank
5
Schläfli Type
{4,6,4,2}
Vertices, edges, …
4, 24, 24, 8, 2
Order of s0s1s2s3s4
6
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (  1,  9)(  2, 10)(  3, 11)(  4, 12)(  5, 13)(  6, 14)(  7, 15)(  8, 16)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)(152,160)(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192);;
s1 := (  2,  3)(  5,  9)(  6, 11)(  7, 10)(  8, 12)( 14, 15)( 17, 33)( 18, 35)( 19, 34)( 20, 36)( 21, 41)( 22, 43)( 23, 42)( 24, 44)( 25, 37)( 26, 39)( 27, 38)( 28, 40)( 29, 45)( 30, 47)( 31, 46)( 32, 48)( 50, 51)( 53, 57)( 54, 59)( 55, 58)( 56, 60)( 62, 63)( 65, 81)( 66, 83)( 67, 82)( 68, 84)( 69, 89)( 70, 91)( 71, 90)( 72, 92)( 73, 85)( 74, 87)( 75, 86)( 76, 88)( 77, 93)( 78, 95)( 79, 94)( 80, 96)( 98, 99)(101,105)(102,107)(103,106)(104,108)(110,111)(113,129)(114,131)(115,130)(116,132)(117,137)(118,139)(119,138)(120,140)(121,133)(122,135)(123,134)(124,136)(125,141)(126,143)(127,142)(128,144)(146,147)(149,153)(150,155)(151,154)(152,156)(158,159)(161,177)(162,179)(163,178)(164,180)(165,185)(166,187)(167,186)(168,188)(169,181)(170,183)(171,182)(172,184)(173,189)(174,191)(175,190)(176,192);;
s2 := (  1,129)(  2,130)(  3,132)(  4,131)(  5,141)(  6,142)(  7,144)(  8,143)(  9,137)( 10,138)( 11,140)( 12,139)( 13,133)( 14,134)( 15,136)( 16,135)( 17,113)( 18,114)( 19,116)( 20,115)( 21,125)( 22,126)( 23,128)( 24,127)( 25,121)( 26,122)( 27,124)( 28,123)( 29,117)( 30,118)( 31,120)( 32,119)( 33, 97)( 34, 98)( 35,100)( 36, 99)( 37,109)( 38,110)( 39,112)( 40,111)( 41,105)( 42,106)( 43,108)( 44,107)( 45,101)( 46,102)( 47,104)( 48,103)( 49,177)( 50,178)( 51,180)( 52,179)( 53,189)( 54,190)( 55,192)( 56,191)( 57,185)( 58,186)( 59,188)( 60,187)( 61,181)( 62,182)( 63,184)( 64,183)( 65,161)( 66,162)( 67,164)( 68,163)( 69,173)( 70,174)( 71,176)( 72,175)( 73,169)( 74,170)( 75,172)( 76,171)( 77,165)( 78,166)( 79,168)( 80,167)( 81,145)( 82,146)( 83,148)( 84,147)( 85,157)( 86,158)( 87,160)( 88,159)( 89,153)( 90,154)( 91,156)( 92,155)( 93,149)( 94,150)( 95,152)( 96,151);;
s3 := (  1, 52)(  2, 51)(  3, 50)(  4, 49)(  5, 56)(  6, 55)(  7, 54)(  8, 53)(  9, 60)( 10, 59)( 11, 58)( 12, 57)( 13, 64)( 14, 63)( 15, 62)( 16, 61)( 17, 68)( 18, 67)( 19, 66)( 20, 65)( 21, 72)( 22, 71)( 23, 70)( 24, 69)( 25, 76)( 26, 75)( 27, 74)( 28, 73)( 29, 80)( 30, 79)( 31, 78)( 32, 77)( 33, 84)( 34, 83)( 35, 82)( 36, 81)( 37, 88)( 38, 87)( 39, 86)( 40, 85)( 41, 92)( 42, 91)( 43, 90)( 44, 89)( 45, 96)( 46, 95)( 47, 94)( 48, 93)( 97,148)( 98,147)( 99,146)(100,145)(101,152)(102,151)(103,150)(104,149)(105,156)(106,155)(107,154)(108,153)(109,160)(110,159)(111,158)(112,157)(113,164)(114,163)(115,162)(116,161)(117,168)(118,167)(119,166)(120,165)(121,172)(122,171)(123,170)(124,169)(125,176)(126,175)(127,174)(128,173)(129,180)(130,179)(131,178)(132,177)(133,184)(134,183)(135,182)(136,181)(137,188)(138,187)(139,186)(140,185)(141,192)(142,191)(143,190)(144,189);;
s4 := (193,194);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(194)!(  1,  9)(  2, 10)(  3, 11)(  4, 12)(  5, 13)(  6, 14)(  7, 15)(  8, 16)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)(152,160)(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192);
s1 := Sym(194)!(  2,  3)(  5,  9)(  6, 11)(  7, 10)(  8, 12)( 14, 15)( 17, 33)( 18, 35)( 19, 34)( 20, 36)( 21, 41)( 22, 43)( 23, 42)( 24, 44)( 25, 37)( 26, 39)( 27, 38)( 28, 40)( 29, 45)( 30, 47)( 31, 46)( 32, 48)( 50, 51)( 53, 57)( 54, 59)( 55, 58)( 56, 60)( 62, 63)( 65, 81)( 66, 83)( 67, 82)( 68, 84)( 69, 89)( 70, 91)( 71, 90)( 72, 92)( 73, 85)( 74, 87)( 75, 86)( 76, 88)( 77, 93)( 78, 95)( 79, 94)( 80, 96)( 98, 99)(101,105)(102,107)(103,106)(104,108)(110,111)(113,129)(114,131)(115,130)(116,132)(117,137)(118,139)(119,138)(120,140)(121,133)(122,135)(123,134)(124,136)(125,141)(126,143)(127,142)(128,144)(146,147)(149,153)(150,155)(151,154)(152,156)(158,159)(161,177)(162,179)(163,178)(164,180)(165,185)(166,187)(167,186)(168,188)(169,181)(170,183)(171,182)(172,184)(173,189)(174,191)(175,190)(176,192);
s2 := Sym(194)!(  1,129)(  2,130)(  3,132)(  4,131)(  5,141)(  6,142)(  7,144)(  8,143)(  9,137)( 10,138)( 11,140)( 12,139)( 13,133)( 14,134)( 15,136)( 16,135)( 17,113)( 18,114)( 19,116)( 20,115)( 21,125)( 22,126)( 23,128)( 24,127)( 25,121)( 26,122)( 27,124)( 28,123)( 29,117)( 30,118)( 31,120)( 32,119)( 33, 97)( 34, 98)( 35,100)( 36, 99)( 37,109)( 38,110)( 39,112)( 40,111)( 41,105)( 42,106)( 43,108)( 44,107)( 45,101)( 46,102)( 47,104)( 48,103)( 49,177)( 50,178)( 51,180)( 52,179)( 53,189)( 54,190)( 55,192)( 56,191)( 57,185)( 58,186)( 59,188)( 60,187)( 61,181)( 62,182)( 63,184)( 64,183)( 65,161)( 66,162)( 67,164)( 68,163)( 69,173)( 70,174)( 71,176)( 72,175)( 73,169)( 74,170)( 75,172)( 76,171)( 77,165)( 78,166)( 79,168)( 80,167)( 81,145)( 82,146)( 83,148)( 84,147)( 85,157)( 86,158)( 87,160)( 88,159)( 89,153)( 90,154)( 91,156)( 92,155)( 93,149)( 94,150)( 95,152)( 96,151);
s3 := Sym(194)!(  1, 52)(  2, 51)(  3, 50)(  4, 49)(  5, 56)(  6, 55)(  7, 54)(  8, 53)(  9, 60)( 10, 59)( 11, 58)( 12, 57)( 13, 64)( 14, 63)( 15, 62)( 16, 61)( 17, 68)( 18, 67)( 19, 66)( 20, 65)( 21, 72)( 22, 71)( 23, 70)( 24, 69)( 25, 76)( 26, 75)( 27, 74)( 28, 73)( 29, 80)( 30, 79)( 31, 78)( 32, 77)( 33, 84)( 34, 83)( 35, 82)( 36, 81)( 37, 88)( 38, 87)( 39, 86)( 40, 85)( 41, 92)( 42, 91)( 43, 90)( 44, 89)( 45, 96)( 46, 95)( 47, 94)( 48, 93)( 97,148)( 98,147)( 99,146)(100,145)(101,152)(102,151)(103,150)(104,149)(105,156)(106,155)(107,154)(108,153)(109,160)(110,159)(111,158)(112,157)(113,164)(114,163)(115,162)(116,161)(117,168)(118,167)(119,166)(120,165)(121,172)(122,171)(123,170)(124,169)(125,176)(126,175)(127,174)(128,173)(129,180)(130,179)(131,178)(132,177)(133,184)(134,183)(135,182)(136,181)(137,188)(138,187)(139,186)(140,185)(141,192)(142,191)(143,190)(144,189);
s4 := Sym(194)!(193,194);
poly := sub<Sym(194)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2 >;