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

Overview

Group: SmallGroup(1920,237638)
Rank: 3
Schläfli Type: {8,30}
Vertices, edges, …: 32, 480, 120
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

Quotients maximal quotients in bold

2-fold

{4,30}*960a

5-fold

{8,6}*384c

8-fold

{4,30}*240b

10-fold

{4,6}*192a

16-fold

{4,15}*120

40-fold

{4,6}*48c

80-fold

{4,3}*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)^15> of order 2

60 facets

60 of {8}*16

20 vertex figures

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

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

60 facets

60 of {8}*16

16 vertex figures

16 of {30}*60

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

30 facets

30 of {8}*16

8 vertex figures

8 of {30}*60

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

30 facets

30 of {8}*16

12 vertex figures

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

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.