Polytope of Type {30,8} with group SmallGroup(1920,237638)

Overview

Group: SmallGroup(1920,237638)
Rank: 3
Schläfli Type: {30,8}
Vertices, edges, …: 120, 480, 32
Order of s₀s₁s₂: 30
Order of s₀s₁s₂s₁: 4
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Self-Petrie

Quotients maximal quotients in bold

2-fold

{30,4}*960a

5-fold

{6,8}*384c

8-fold

{30,4}*240b

10-fold

{6,4}*192a

16-fold

{15,4}*120

40-fold

{6,4}*48c

80-fold

{3,4}*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=<(s0*s1)^15> of order 2

20 facets

8 of {15}*30
12 of {30}*60

60 vertex figures

60 of {8}*16

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

16 facets

16 of {30}*60

60 vertex figures

60 of {8}*16

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

8 facets

8 of {30}*60

30 vertex figures

30 of {8}*16

P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2, (s0*s1)^15> of order 4

12 facets

8 of {15}*30
4 of {30}*60

30 vertex figures

30 of {8}*16

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.