Polytope of Type {48,4} with group SmallGroup(384,1684)

Overview

Group: SmallGroup(384,1684)
Rank: 3
Schläfli Type: {48,4}
Vertices, edges, …: 48, 96, 4
Order of s₀s₁s₂: 48
Order of s₀s₁s₂s₁: 2
Also known as: {48,4|2}. if this polytope has another name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie

Quotients maximal quotients in bold

2-fold

3-fold

{16,4}*128a

4-fold

6-fold

8-fold

12-fold

16-fold

{6,2}*24

24-fold

32-fold

{3,2}*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

None.

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References