Polytope of Type {16,4,3} with group SmallGroup(768,1088585)

Overview

Group: SmallGroup(768,1088585)
Rank: 4
Schläfli Type: {16,4,3}
Vertices, edges, …: 16, 64, 12, 6
Order of s₀s₁s₂s₃: 48
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: {{16,4|2},{4,3}}. if this polytope has another name.

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

2-fold

{8,4,3}*384

4-fold

8-fold

16-fold

32-fold

{2,2,3}*24

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s1*s2)^2> of order 2

4 facets

2 of {16,2}*64
2 of {16,4}*128a

16 vertex figures

16 of 2-fold non-regular quotient of {4,3}*48

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.