Polytope of Type {24,12} with group SmallGroup(768,1087755)

Overview

Group: SmallGroup(768,1087755)
Rank: 3
Schläfli Type: {24,12}
Vertices, edges, …: 32, 192, 16
Order of s₀s₁s₂: 8
Order of s₀s₁s₂s₁: 6
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

{6,6}*96

12-fold

{8,4}*64a

16-fold

24-fold

32-fold

{3,3}*24

48-fold

96-fold

{2,2}*8

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References