Overview
- Group
- SmallGroup(1728,46100)
- Rank
- 3
- Schläfli Type
- {18,6}
- Vertices, edges, …
- 144, 432, 48
- Order of s0s1s2
- 18
- 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
3-fold
16-fold
48-fold
144-fold
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
24 facets
- 24 of {18}*36
72 vertex figures
- 72 of {6}*12
P/N, where N=<s0*s2*s1*s0*(s2*s1)^2*s0*s1*s0*(s2*s1)^2*s2> of order 2
28 facets
72 vertex figures
- 72 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
14 facets
36 vertex figures
- 36 of {6}*12
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2*s2, (s0*(s2*s1)^2)^2> of order 4
12 facets
- 12 of {18}*36
36 vertex figures
- 36 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
12 facets
- 12 of {18}*36
36 vertex figures
- 36 of {6}*12
P/N, where N=<((s1*s0)^2*s1*s2)^2, (s0*s1*s0*(s2*s1)^2)^2> of order 4
16 facets
36 vertex figures
- 36 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
18 facets
36 vertex figures
- 36 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> of order 8
8 facets
18 vertex figures
- 18 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)( 49,129)( 50,130)( 51,132)( 52,131)( 53,133)( 54,134)( 55,136)( 56,135)( 57,141)( 58,142)( 59,144)( 60,143)( 61,137)( 62,138)( 63,140)( 64,139)( 65,113)( 66,114)( 67,116)( 68,115)( 69,117)( 70,118)( 71,120)( 72,119)( 73,125)( 74,126)( 75,128)( 76,127)( 77,121)( 78,122)( 79,124)( 80,123)( 81, 97)( 82, 98)( 83,100)( 84, 99)( 85,101)( 86,102)( 87,104)( 88,103)( 89,109)( 90,110)( 91,112)( 92,111)( 93,105)( 94,106)( 95,108)( 96,107);; s1 := ( 1, 50)( 2, 49)( 3, 51)( 4, 52)( 5, 62)( 6, 61)( 7, 63)( 8, 64)( 9, 58)( 10, 57)( 11, 59)( 12, 60)( 13, 54)( 14, 53)( 15, 55)( 16, 56)( 17, 82)( 18, 81)( 19, 83)( 20, 84)( 21, 94)( 22, 93)( 23, 95)( 24, 96)( 25, 90)( 26, 89)( 27, 91)( 28, 92)( 29, 86)( 30, 85)( 31, 87)( 32, 88)( 33, 66)( 34, 65)( 35, 67)( 36, 68)( 37, 78)( 38, 77)( 39, 79)( 40, 80)( 41, 74)( 42, 73)( 43, 75)( 44, 76)( 45, 70)( 46, 69)( 47, 71)( 48, 72)( 97,130)( 98,129)( 99,131)(100,132)(101,142)(102,141)(103,143)(104,144)(105,138)(106,137)(107,139)(108,140)(109,134)(110,133)(111,135)(112,136)(113,114)(117,126)(118,125)(119,127)(120,128)(121,122);; s2 := ( 2, 5)( 3, 13)( 4, 9)( 7, 14)( 8, 10)( 11, 16)( 18, 21)( 19, 29)( 20, 25)( 23, 30)( 24, 26)( 27, 32)( 34, 37)( 35, 45)( 36, 41)( 39, 46)( 40, 42)( 43, 48)( 50, 53)( 51, 61)( 52, 57)( 55, 62)( 56, 58)( 59, 64)( 66, 69)( 67, 77)( 68, 73)( 71, 78)( 72, 74)( 75, 80)( 82, 85)( 83, 93)( 84, 89)( 87, 94)( 88, 90)( 91, 96)( 98,101)( 99,109)(100,105)(103,110)(104,106)(107,112)(114,117)(115,125)(116,121)(119,126)(120,122)(123,128)(130,133)(131,141)(132,137)(135,142)(136,138)(139,144);; 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, 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*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(144)!( 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)( 49,129)( 50,130)( 51,132)( 52,131)( 53,133)( 54,134)( 55,136)( 56,135)( 57,141)( 58,142)( 59,144)( 60,143)( 61,137)( 62,138)( 63,140)( 64,139)( 65,113)( 66,114)( 67,116)( 68,115)( 69,117)( 70,118)( 71,120)( 72,119)( 73,125)( 74,126)( 75,128)( 76,127)( 77,121)( 78,122)( 79,124)( 80,123)( 81, 97)( 82, 98)( 83,100)( 84, 99)( 85,101)( 86,102)( 87,104)( 88,103)( 89,109)( 90,110)( 91,112)( 92,111)( 93,105)( 94,106)( 95,108)( 96,107); s1 := Sym(144)!( 1, 50)( 2, 49)( 3, 51)( 4, 52)( 5, 62)( 6, 61)( 7, 63)( 8, 64)( 9, 58)( 10, 57)( 11, 59)( 12, 60)( 13, 54)( 14, 53)( 15, 55)( 16, 56)( 17, 82)( 18, 81)( 19, 83)( 20, 84)( 21, 94)( 22, 93)( 23, 95)( 24, 96)( 25, 90)( 26, 89)( 27, 91)( 28, 92)( 29, 86)( 30, 85)( 31, 87)( 32, 88)( 33, 66)( 34, 65)( 35, 67)( 36, 68)( 37, 78)( 38, 77)( 39, 79)( 40, 80)( 41, 74)( 42, 73)( 43, 75)( 44, 76)( 45, 70)( 46, 69)( 47, 71)( 48, 72)( 97,130)( 98,129)( 99,131)(100,132)(101,142)(102,141)(103,143)(104,144)(105,138)(106,137)(107,139)(108,140)(109,134)(110,133)(111,135)(112,136)(113,114)(117,126)(118,125)(119,127)(120,128)(121,122); s2 := Sym(144)!( 2, 5)( 3, 13)( 4, 9)( 7, 14)( 8, 10)( 11, 16)( 18, 21)( 19, 29)( 20, 25)( 23, 30)( 24, 26)( 27, 32)( 34, 37)( 35, 45)( 36, 41)( 39, 46)( 40, 42)( 43, 48)( 50, 53)( 51, 61)( 52, 57)( 55, 62)( 56, 58)( 59, 64)( 66, 69)( 67, 77)( 68, 73)( 71, 78)( 72, 74)( 75, 80)( 82, 85)( 83, 93)( 84, 89)( 87, 94)( 88, 90)( 91, 96)( 98,101)( 99,109)(100,105)(103,110)(104,106)(107,112)(114,117)(115,125)(116,121)(119,126)(120,122)(123,128)(130,133)(131,141)(132,137)(135,142)(136,138)(139,144); poly := sub<Sym(144)|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, 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*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1, s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1 >;
References
None.
to this polytope.