Polytope of Type {6,6} with group SmallGroup(1152,157852)

Overview

Group: SmallGroup(1152,157852)
Rank: 3
Schläfli Type: {6,6}
Vertices, edges, …: 96, 288, 96
Order of s₀s₁s₂: 6
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

{6,6}*576e

16-fold

{6,6}*72c

32-fold

{3,6}*36

48-fold

{6,2}*24

96-fold

{3,2}*12

144-fold

{2,2}*8

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*s0)^2*s1*s2)^2> of order 2

48 facets

48 of {6}*12

48 vertex figures

48 of {6}*12

P/N, where N=<(s0*s1)^3> of order 2

56 facets

16 of {3}*6
40 of {6}*12

48 vertex figures

48 of {6}*12

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

48 facets

48 of {6}*12

48 vertex figures

48 of {6}*12

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

48 facets

48 of {6}*12

48 vertex figures

48 of {6}*12

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

48 facets

48 of {6}*12

48 vertex figures

48 of {6}*12

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

48 facets

48 of {6}*12

52 vertex figures

44 of {6}*12
8 of {3}*6

P/N, where N=<(s1*s0*s1*s2)^2> of order 3

32 facets

32 of {6}*12

36 vertex figures

30 of {6}*12
6 of {2}*4

P/N, where N=<(s0*s1)^2> of order 3

40 facets

12 of {2}*4
28 of {6}*12

32 vertex figures

32 of {6}*12

P/N, where N=<s0*s1*s2*(s1*s0)^2*(s2*s1)^2*s0*s1*s2, s0*s2*s1*s0*s1*(s2*s1*s0)^2*s1*s2*s1> of order 4

24 facets

24 of {6}*12

24 vertex figures

24 of {6}*12

P/N, where N=<((s1*s0)^2*s1*s2)^2, (s0*s1)^2*(s2*s1)^2*s0*s1*s0*(s2*s1)^2*s2> of order 4

24 facets

24 of {6}*12

28 vertex figures

20 of {6}*12
8 of {3}*6

P/N, where N=<((s1*s0)^2*s1*s2)^2, (s0*s1*s0*(s2*s1)^2)^2> of order 4

24 facets

24 of {6}*12

24 vertex figures

24 of {6}*12

P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2*s2, (s0*(s2*s1)^2)^2> of order 4

24 facets

24 of {6}*12

24 vertex figures

24 of {6}*12

P/N, where N=<s1*s0*s1*s2*s1*s0*(s1*s2)^3, (s0*s1)^2*s2*s1*s0*(s1*s2)^2*s1*s0*s2> of order 4

24 facets

24 of {6}*12

24 vertex figures

24 of {6}*12

P/N, where N=<s1*s0*(s2*s1)^2*s0*s2*s1*s2, s0*s1*s0*(s2*s1)^2*s0*s2*s1*s0*s2> of order 4

24 facets

24 of {6}*12

24 vertex figures

24 of {6}*12

P/N, where N=<((s1*s0)^2*s1*s2)^2, (s0*s1*s0*(s2*s1)^2)^2*s2> of order 4

24 facets

24 of {6}*12

24 vertex figures

24 of {6}*12

P/N, where N=<((s1*s0)^2*s1*s2)^2, (s1*s0)^2*s2*s1*s0*(s2*s1)^2*s2> of order 4

24 facets

24 of {6}*12

24 vertex figures

24 of {6}*12

P/N, where N=<s0*s2*(s1*s0)^2*s1*s2, s1*s0*(s1*s2)^2*(s1*s0)^2*(s2*s1)^2> of order 4

28 facets

20 of {6}*12
8 of {3}*6

24 vertex figures

24 of {6}*12

P/N, where N=<s0*s1*s0*s2*s1*s0*(s1*s2)^3, s0*(s1*s2)^2*(s1*s0*s2)^2*s1> of order 4

24 facets

24 of {6}*12

24 vertex figures

24 of {6}*12

P/N, where N=<(s0*s1)^3, s0*s2*(s1*s0)^2*s1*s2> of order 4

32 facets

16 of {3}*6
16 of {6}*12

24 vertex figures

24 of {6}*12

P/N, where N=<(s0*s1)^2*(s2*s1)^2*s0*s2*s1*s2, s0*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1> of order 4

24 facets

24 of {6}*12

24 vertex figures

24 of {6}*12

P/N, where N=<s0*(s1*s2)^2*(s1*s0*s2)^2*s1, ((s1*s0)^2*s1*s2)^2> of order 4

28 facets

20 of {6}*12
8 of {3}*6

24 vertex figures

24 of {6}*12

P/N, where N=<((s1*s0)^2*s1*s2)^2, s1*s0*(s1*s2)^2*(s1*s0)^2*(s2*s1)^2*s2> of order 4

24 facets

24 of {6}*12

24 vertex figures

24 of {6}*12

P/N, where N=<((s1*s0)^2*s1*s2)^2, (s0*s1)^2*s0*s2*s1*s0*(s2*s1)^2*s2> of order 4

24 facets

24 of {6}*12

24 vertex figures

24 of {6}*12

P/N, where N=<s2*s1*s0*s2*(s1*s0)^2*(s1*s2)^2, s0*s2*s1*s0*s2*(s1*s0)^2*s1*s2*s1*s0*s2> of order 4

32 facets

16 of {6}*12
16 of {3}*6

24 vertex figures

24 of {6}*12

P/N, where N=<(s1*s0*s1*s2)^2, s0*(s1*s2)^2*(s1*s0)^2*(s1*s2)^3> of order 6

16 facets

16 of {6}*12

18 vertex figures

15 of {6}*12
3 of {2}*4

P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s1*s2*s1*s0, s0*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1, (s0*s2*s1)^2*s0*(s1*s2)^2*s1> of order 8

14 facets

10 of {6}*12
4 of {3}*6

12 vertex figures

12 of {6}*12

P/N, where N=<s0*s2*(s1*s0)^2*s1*s2, s1*s0*s1*s2*s1*s0*(s1*s2)^3, (s0*s1)^2*s2*s1*s0*(s1*s2)^2*s1*s0*s2> of order 8

18 facets

6 of {6}*12
12 of {3}*6

12 vertex figures

12 of {6}*12

P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2, s1*s0*(s2*s1)^2*s0*s2*s1*s2> of order 8

12 facets

12 of {6}*12

12 vertex figures

12 of {6}*12

P/N, where N=<(s0*s1)^3, s0*s2*(s1*s0)^2*s1*s2, s0*s1*s2*s1*s0*(s2*s1)^2*s2> of order 8

16 facets

8 of {3}*6
8 of {6}*12

12 vertex figures

12 of {6}*12

P/N, where N=<s1*s0*(s2*s1)^2*s0*s2*s1*s2, (s1*s0)^2*s2*s1*s0*(s2*s1)^2, s0*s1*s0*(s2*s1)^2*s0*s2*s1*s0*s2> of order 8

12 facets

12 of {6}*12

12 vertex figures

12 of {6}*12

P/N, where N=<(s0*s1)^3, s0*s2*(s1*s0)^2*s1*s2, s1*s0*(s2*s1)^2*s0*s2*s1*s2> of order 8

16 facets

8 of {3}*6
8 of {6}*12

12 vertex figures

12 of {6}*12

P/N, where N=<(s0*s1)^2*(s2*s1)^2*s0*s2*s1*s2, s0*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1, (s1*s0)^2*s2*s1*s0*(s2*s1)^2*s2> of order 8

12 facets

12 of {6}*12

12 vertex figures

12 of {6}*12

P/N, where N=<s0*s1*s0*s2*s1*s0*(s1*s2)^3, s0*(s1*s2)^2*(s1*s0*s2)^2*s1, ((s1*s0)^2*s1*s2)^2> of order 8

16 facets

8 of {6}*12
8 of {3}*6

12 vertex figures

12 of {6}*12

P/N, where N=<s1*s0*(s1*s2)^2*s1*s0*s2*s1*s2, (s0*s1)^2*s0*s2*s1*s0*(s2*s1)^2*s2> of order 8

12 facets

12 of {6}*12

12 vertex figures

12 of {6}*12

P/N, where N=<s0*s2*(s1*s0)^2*s1*s2, s0*s1*s0*s2*s1*s0*(s1*s2)^3, s0*(s1*s2)^2*(s1*s0*s2)^2*s1> of order 8

14 facets

10 of {6}*12
4 of {3}*6

12 vertex figures

12 of {6}*12

P/N, where N=<((s1*s0)^2*s1*s2)^2, s1*s0*s1*s2*s1*s0*(s1*s2)^3, (s0*s1)^2*s2*s1*s0*(s1*s2)^2*s1*s0*s2> of order 8

12 facets

12 of {6}*12

12 vertex figures

12 of {6}*12

P/N, where N=<s1*s0*(s1*s2)^2*s1*s0*s2*s1, (s0*s1)^2*(s2*s1)^2*s0*s2*s1*s0, (s0*s1)^2*s0*s2*s1*s0*(s2*s1)^2*s2> of order 8

12 facets

12 of {6}*12

14 vertex figures

10 of {6}*12
4 of {3}*6

P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2*s2, (s0*(s2*s1)^2)^2, s1*s0*(s2*s1)^2*s0*s2*s1*s2> of order 8

12 facets

12 of {6}*12

12 vertex figures

12 of {6}*12

P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2*s2, (s0*(s2*s1)^2)^2, s1*s0*(s1*s2)^2*s1*s0*s2*s1> of order 8

12 facets

12 of {6}*12

16 vertex figures

8 of {6}*12
8 of {3}*6

P/N, where N=<(s1*s0)^2*s2*s1*s0*(s2*s1)^2, (s0*s1)^2*(s2*s1)^2*s0*s2*s1*s2> of order 8

12 facets

12 of {6}*12

12 vertex figures

12 of {6}*12

P/N, where N=<(s0*s1)^3, s0*s2*(s1*s0)^2*s1*s2, s1*s0*(s2*s1)^2*s0*s1*s0*(s2*s1)^2*s2> of order 8

16 facets

8 of {3}*6
8 of {6}*12

14 vertex figures

10 of {6}*12
4 of {3}*6

P/N, where N=<(s0*s1)^3, s0*s2*(s1*s0)^2*s1*s2, (s0*s1*s0*(s2*s1)^2)^2*s2> of order 8

16 facets

8 of {3}*6
8 of {6}*12

12 vertex figures

12 of {6}*12

P/N, where N=<(s1*s0*s1*s2)^2, s0*s1*s2*s1*s0*(s2*s1)^2*s2> of order 12

8 facets

8 of {6}*12

12 vertex figures

6 of {6}*12
6 of {2}*4

P/N, where N=<(s0*s1*s2*s1)^2, (s1*s0*s1*s2)^2> of order 12

8 facets

8 of {6}*12

12 vertex figures

6 of {6}*12
6 of {2}*4

P/N, where N=<s0*s2*s1*s0*s1*s2, s1*s0*s2*s1*s0*s1*s2*s1> of order 12

16 facets

4 of {6}*12
12 of {2}*4

8 vertex figures

8 of {6}*12

P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2*s2, (s0*(s2*s1)^2)^2, s1*s0*(s2*s1)^2*s0*s2*s1*s2, s1*s0*s1*s2*s1*s0*(s1*s2)^2*s1> of order 16

6 facets

6 of {6}*12

6 vertex figures

6 of {6}*12

P/N, where N=<s1*s0*s2*(s1*s0)^2*s1*s2*s1, (s0*s1)^2*(s2*s1)^2*s0*s2*s1*s2, s0*s1*s0*s2*(s1*s0)^2*s1*s2*s1*s0, s0*(s1*s2)^2*(s1*s0)^2*s2*s1*s2> of order 16

8 facets

4 of {6}*12
4 of {3}*6

6 vertex figures

6 of {6}*12

P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2*s2, (s0*(s2*s1)^2)^2, s1*s0*s2*(s1*s0)^2*s1*s2*s1, s1*s0*(s2*s1)^2*s0*s2*s1*s2> of order 16

10 facets

2 of {6}*12
8 of {3}*6

6 vertex figures

6 of {6}*12

P/N, where N=<(s0*s1)^3, s0*s2*(s1*s0)^2*s1*s2, s0*s1*s0*(s2*s1)^2*s0*s2*s1, s0*s1*s2*s1*s0*(s2*s1)^2*s2> of order 16

8 facets

4 of {3}*6
4 of {6}*12

8 vertex figures

4 of {6}*12
4 of {3}*6

P/N, where N=<(s0*s1)^3, s0*s2*(s1*s0)^2*s1*s2, s0*s1*s2*s1*s0*(s2*s1)^2, s1*s0*(s2*s1)^2*s0*s2*s1*s2> of order 16

8 facets

4 of {3}*6
4 of {6}*12

6 vertex figures

6 of {6}*12

Representations

Permutation Representation (GAP)

s0 := (  3,  4)(  7,  8)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)( 26, 46)( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 49, 97)( 50, 98)( 51,100)( 52, 99)( 53,101)( 54,102)( 55,104)( 56,103)( 57,109)( 58,110)( 59,112)( 60,111)( 61,105)( 62,106)( 63,108)( 64,107)( 65,129)( 66,130)( 67,132)( 68,131)( 69,133)( 70,134)( 71,136)( 72,135)( 73,141)( 74,142)( 75,144)( 76,143)( 77,137)( 78,138)( 79,140)( 80,139)( 81,113)( 82,114)( 83,116)( 84,115)( 85,117)( 86,118)( 87,120)( 88,119)( 89,125)( 90,126)( 91,128)( 92,127)( 93,121)( 94,122)( 95,124)( 96,123)(147,148)(151,152)(153,157)(154,158)(155,160)(156,159)(161,177)(162,178)(163,180)(164,179)(165,181)(166,182)(167,184)(168,183)(169,189)(170,190)(171,192)(172,191)(173,185)(174,186)(175,188)(176,187)(193,241)(194,242)(195,244)(196,243)(197,245)(198,246)(199,248)(200,247)(201,253)(202,254)(203,256)(204,255)(205,249)(206,250)(207,252)(208,251)(209,273)(210,274)(211,276)(212,275)(213,277)(214,278)(215,280)(216,279)(217,285)(218,286)(219,288)(220,287)(221,281)(222,282)(223,284)(224,283)(225,257)(226,258)(227,260)(228,259)(229,261)(230,262)(231,264)(232,263)(233,269)(234,270)(235,272)(236,271)(237,265)(238,266)(239,268)(240,267);;
s1 := (  1,194)(  2,193)(  3,195)(  4,196)(  5,206)(  6,205)(  7,207)(  8,208)(  9,202)( 10,201)( 11,203)( 12,204)( 13,198)( 14,197)( 15,199)( 16,200)( 17,226)( 18,225)( 19,227)( 20,228)( 21,238)( 22,237)( 23,239)( 24,240)( 25,234)( 26,233)( 27,235)( 28,236)( 29,230)( 30,229)( 31,231)( 32,232)( 33,210)( 34,209)( 35,211)( 36,212)( 37,222)( 38,221)( 39,223)( 40,224)( 41,218)( 42,217)( 43,219)( 44,220)( 45,214)( 46,213)( 47,215)( 48,216)( 49,146)( 50,145)( 51,147)( 52,148)( 53,158)( 54,157)( 55,159)( 56,160)( 57,154)( 58,153)( 59,155)( 60,156)( 61,150)( 62,149)( 63,151)( 64,152)( 65,178)( 66,177)( 67,179)( 68,180)( 69,190)( 70,189)( 71,191)( 72,192)( 73,186)( 74,185)( 75,187)( 76,188)( 77,182)( 78,181)( 79,183)( 80,184)( 81,162)( 82,161)( 83,163)( 84,164)( 85,174)( 86,173)( 87,175)( 88,176)( 89,170)( 90,169)( 91,171)( 92,172)( 93,166)( 94,165)( 95,167)( 96,168)( 97,242)( 98,241)( 99,243)(100,244)(101,254)(102,253)(103,255)(104,256)(105,250)(106,249)(107,251)(108,252)(109,246)(110,245)(111,247)(112,248)(113,274)(114,273)(115,275)(116,276)(117,286)(118,285)(119,287)(120,288)(121,282)(122,281)(123,283)(124,284)(125,278)(126,277)(127,279)(128,280)(129,258)(130,257)(131,259)(132,260)(133,270)(134,269)(135,271)(136,272)(137,266)(138,265)(139,267)(140,268)(141,262)(142,261)(143,263)(144,264);;
s2 := (  2,  5)(  3,  9)(  4, 13)(  7, 10)(  8, 14)( 12, 15)( 17, 33)( 18, 37)( 19, 41)( 20, 45)( 21, 34)( 22, 38)( 23, 42)( 24, 46)( 25, 35)( 26, 39)( 27, 43)( 28, 47)( 29, 36)( 30, 40)( 31, 44)( 32, 48)( 49, 65)( 50, 69)( 51, 73)( 52, 77)( 53, 66)( 54, 70)( 55, 74)( 56, 78)( 57, 67)( 58, 71)( 59, 75)( 60, 79)( 61, 68)( 62, 72)( 63, 76)( 64, 80)( 82, 85)( 83, 89)( 84, 93)( 87, 90)( 88, 94)( 92, 95)( 97,129)( 98,133)( 99,137)(100,141)(101,130)(102,134)(103,138)(104,142)(105,131)(106,135)(107,139)(108,143)(109,132)(110,136)(111,140)(112,144)(114,117)(115,121)(116,125)(119,122)(120,126)(124,127)(146,149)(147,153)(148,157)(151,154)(152,158)(156,159)(161,177)(162,181)(163,185)(164,189)(165,178)(166,182)(167,186)(168,190)(169,179)(170,183)(171,187)(172,191)(173,180)(174,184)(175,188)(176,192)(193,209)(194,213)(195,217)(196,221)(197,210)(198,214)(199,218)(200,222)(201,211)(202,215)(203,219)(204,223)(205,212)(206,216)(207,220)(208,224)(226,229)(227,233)(228,237)(231,234)(232,238)(236,239)(241,273)(242,277)(243,281)(244,285)(245,274)(246,278)(247,282)(248,286)(249,275)(250,279)(251,283)(252,287)(253,276)(254,280)(255,284)(256,288)(258,261)(259,265)(260,269)(263,266)(264,270)(268,271);;
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*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(288)!(  3,  4)(  7,  8)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)( 26, 46)( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 49, 97)( 50, 98)( 51,100)( 52, 99)( 53,101)( 54,102)( 55,104)( 56,103)( 57,109)( 58,110)( 59,112)( 60,111)( 61,105)( 62,106)( 63,108)( 64,107)( 65,129)( 66,130)( 67,132)( 68,131)( 69,133)( 70,134)( 71,136)( 72,135)( 73,141)( 74,142)( 75,144)( 76,143)( 77,137)( 78,138)( 79,140)( 80,139)( 81,113)( 82,114)( 83,116)( 84,115)( 85,117)( 86,118)( 87,120)( 88,119)( 89,125)( 90,126)( 91,128)( 92,127)( 93,121)( 94,122)( 95,124)( 96,123)(147,148)(151,152)(153,157)(154,158)(155,160)(156,159)(161,177)(162,178)(163,180)(164,179)(165,181)(166,182)(167,184)(168,183)(169,189)(170,190)(171,192)(172,191)(173,185)(174,186)(175,188)(176,187)(193,241)(194,242)(195,244)(196,243)(197,245)(198,246)(199,248)(200,247)(201,253)(202,254)(203,256)(204,255)(205,249)(206,250)(207,252)(208,251)(209,273)(210,274)(211,276)(212,275)(213,277)(214,278)(215,280)(216,279)(217,285)(218,286)(219,288)(220,287)(221,281)(222,282)(223,284)(224,283)(225,257)(226,258)(227,260)(228,259)(229,261)(230,262)(231,264)(232,263)(233,269)(234,270)(235,272)(236,271)(237,265)(238,266)(239,268)(240,267);
s1 := Sym(288)!(  1,194)(  2,193)(  3,195)(  4,196)(  5,206)(  6,205)(  7,207)(  8,208)(  9,202)( 10,201)( 11,203)( 12,204)( 13,198)( 14,197)( 15,199)( 16,200)( 17,226)( 18,225)( 19,227)( 20,228)( 21,238)( 22,237)( 23,239)( 24,240)( 25,234)( 26,233)( 27,235)( 28,236)( 29,230)( 30,229)( 31,231)( 32,232)( 33,210)( 34,209)( 35,211)( 36,212)( 37,222)( 38,221)( 39,223)( 40,224)( 41,218)( 42,217)( 43,219)( 44,220)( 45,214)( 46,213)( 47,215)( 48,216)( 49,146)( 50,145)( 51,147)( 52,148)( 53,158)( 54,157)( 55,159)( 56,160)( 57,154)( 58,153)( 59,155)( 60,156)( 61,150)( 62,149)( 63,151)( 64,152)( 65,178)( 66,177)( 67,179)( 68,180)( 69,190)( 70,189)( 71,191)( 72,192)( 73,186)( 74,185)( 75,187)( 76,188)( 77,182)( 78,181)( 79,183)( 80,184)( 81,162)( 82,161)( 83,163)( 84,164)( 85,174)( 86,173)( 87,175)( 88,176)( 89,170)( 90,169)( 91,171)( 92,172)( 93,166)( 94,165)( 95,167)( 96,168)( 97,242)( 98,241)( 99,243)(100,244)(101,254)(102,253)(103,255)(104,256)(105,250)(106,249)(107,251)(108,252)(109,246)(110,245)(111,247)(112,248)(113,274)(114,273)(115,275)(116,276)(117,286)(118,285)(119,287)(120,288)(121,282)(122,281)(123,283)(124,284)(125,278)(126,277)(127,279)(128,280)(129,258)(130,257)(131,259)(132,260)(133,270)(134,269)(135,271)(136,272)(137,266)(138,265)(139,267)(140,268)(141,262)(142,261)(143,263)(144,264);
s2 := Sym(288)!(  2,  5)(  3,  9)(  4, 13)(  7, 10)(  8, 14)( 12, 15)( 17, 33)( 18, 37)( 19, 41)( 20, 45)( 21, 34)( 22, 38)( 23, 42)( 24, 46)( 25, 35)( 26, 39)( 27, 43)( 28, 47)( 29, 36)( 30, 40)( 31, 44)( 32, 48)( 49, 65)( 50, 69)( 51, 73)( 52, 77)( 53, 66)( 54, 70)( 55, 74)( 56, 78)( 57, 67)( 58, 71)( 59, 75)( 60, 79)( 61, 68)( 62, 72)( 63, 76)( 64, 80)( 82, 85)( 83, 89)( 84, 93)( 87, 90)( 88, 94)( 92, 95)( 97,129)( 98,133)( 99,137)(100,141)(101,130)(102,134)(103,138)(104,142)(105,131)(106,135)(107,139)(108,143)(109,132)(110,136)(111,140)(112,144)(114,117)(115,121)(116,125)(119,122)(120,126)(124,127)(146,149)(147,153)(148,157)(151,154)(152,158)(156,159)(161,177)(162,181)(163,185)(164,189)(165,178)(166,182)(167,186)(168,190)(169,179)(170,183)(171,187)(172,191)(173,180)(174,184)(175,188)(176,192)(193,209)(194,213)(195,217)(196,221)(197,210)(198,214)(199,218)(200,222)(201,211)(202,215)(203,219)(204,223)(205,212)(206,216)(207,220)(208,224)(226,229)(227,233)(228,237)(231,234)(232,238)(236,239)(241,273)(242,277)(243,281)(244,285)(245,274)(246,278)(247,282)(248,286)(249,275)(250,279)(251,283)(252,287)(253,276)(254,280)(255,284)(256,288)(258,261)(259,265)(260,269)(263,266)(264,270)(268,271);
poly := sub<Sym(288)|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*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 >;

References

None.

to this polytope.

Overview

Special Properties

Related Polytopes

Quotients maximal quotients in bold

Covers minimal covers in bold

Irregular Quotients of which this is a minimal cover

Representations

References

Twisty Puzzle