Polytope of Type {4,24} with group SmallGroup(384,18015)

Overview

Group: SmallGroup(384,18015)
Rank: 3
Schläfli Type: {4,24}
Vertices, edges, …: 8, 96, 48
Order of s₀s₁s₂: 24
Order of s₀s₁s₂s₁: 4
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

12-fold

{2,8}*32

16-fold

24-fold

{2,4}*16

32-fold

{2,3}*12

48-fold

{2,2}*8

Covers minimal covers in bold

2-fold

3-fold

5-fold

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<s0*s2*s1*s0*s1*s2> of order 2

32 facets

16 of {4}*8
16 of {2}*4

4 vertex figures

4 of {24}*48

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.