Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,48,4}

Atlas Canonical Name {2,48,4}*768b

Overview

Group
SmallGroup(768,323454)
Rank
4
Schläfli Type
{2,48,4}
Vertices, edges, …
2, 48, 96, 4
Order of s0s1s2s3
48
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

3-fold

4-fold

6-fold

8-fold

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