Overview
- Group
- SmallGroup(576,2907)
- Rank
- 3
- Schläfli Type
- {6,48}
- Vertices, edges, …
- 6, 144, 48
- Order of s0s1s2
- 48
- Order of s0s1s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
8-fold
9-fold
12-fold
16-fold
18-fold
24-fold
36-fold
48-fold
72-fold
Covers minimal covers in bold
2-fold
3-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 29, 30)( 31, 34)( 32, 36)( 33, 35)( 38, 39)( 40, 43)( 41, 45)( 42, 44)( 47, 48)( 49, 52)( 50, 54)( 51, 53)( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 65, 66)( 67, 70)( 68, 72)( 69, 71)( 74, 75)( 76, 79)( 77, 81)( 78, 80)( 83, 84)( 85, 88)( 86, 90)( 87, 89)( 92, 93)( 94, 97)( 95, 99)( 96, 98)(101,102)(103,106)(104,108)(105,107)(110,111)(112,115)(113,117)(114,116)(119,120)(121,124)(122,126)(123,125)(128,129)(130,133)(131,135)(132,134)(137,138)(139,142)(140,144)(141,143);; s1 := ( 1, 77)( 2, 76)( 3, 78)( 4, 74)( 5, 73)( 6, 75)( 7, 80)( 8, 79)( 9, 81)( 10, 86)( 11, 85)( 12, 87)( 13, 83)( 14, 82)( 15, 84)( 16, 89)( 17, 88)( 18, 90)( 19,104)( 20,103)( 21,105)( 22,101)( 23,100)( 24,102)( 25,107)( 26,106)( 27,108)( 28, 95)( 29, 94)( 30, 96)( 31, 92)( 32, 91)( 33, 93)( 34, 98)( 35, 97)( 36, 99)( 37,131)( 38,130)( 39,132)( 40,128)( 41,127)( 42,129)( 43,134)( 44,133)( 45,135)( 46,140)( 47,139)( 48,141)( 49,137)( 50,136)( 51,138)( 52,143)( 53,142)( 54,144)( 55,113)( 56,112)( 57,114)( 58,110)( 59,109)( 60,111)( 61,116)( 62,115)( 63,117)( 64,122)( 65,121)( 66,123)( 67,119)( 68,118)( 69,120)( 70,125)( 71,124)( 72,126);; s2 := ( 2, 3)( 5, 6)( 8, 9)( 11, 12)( 14, 15)( 17, 18)( 19, 28)( 20, 30)( 21, 29)( 22, 31)( 23, 33)( 24, 32)( 25, 34)( 26, 36)( 27, 35)( 37, 55)( 38, 57)( 39, 56)( 40, 58)( 41, 60)( 42, 59)( 43, 61)( 44, 63)( 45, 62)( 46, 64)( 47, 66)( 48, 65)( 49, 67)( 50, 69)( 51, 68)( 52, 70)( 53, 72)( 54, 71)( 73,109)( 74,111)( 75,110)( 76,112)( 77,114)( 78,113)( 79,115)( 80,117)( 81,116)( 82,118)( 83,120)( 84,119)( 85,121)( 86,123)( 87,122)( 88,124)( 89,126)( 90,125)( 91,136)( 92,138)( 93,137)( 94,139)( 95,141)( 96,140)( 97,142)( 98,144)( 99,143)(100,127)(101,129)(102,128)(103,130)(104,132)(105,131)(106,133)(107,135)(108,134);; 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*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*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*s0*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(144)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 29, 30)( 31, 34)( 32, 36)( 33, 35)( 38, 39)( 40, 43)( 41, 45)( 42, 44)( 47, 48)( 49, 52)( 50, 54)( 51, 53)( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 65, 66)( 67, 70)( 68, 72)( 69, 71)( 74, 75)( 76, 79)( 77, 81)( 78, 80)( 83, 84)( 85, 88)( 86, 90)( 87, 89)( 92, 93)( 94, 97)( 95, 99)( 96, 98)(101,102)(103,106)(104,108)(105,107)(110,111)(112,115)(113,117)(114,116)(119,120)(121,124)(122,126)(123,125)(128,129)(130,133)(131,135)(132,134)(137,138)(139,142)(140,144)(141,143); s1 := Sym(144)!( 1, 77)( 2, 76)( 3, 78)( 4, 74)( 5, 73)( 6, 75)( 7, 80)( 8, 79)( 9, 81)( 10, 86)( 11, 85)( 12, 87)( 13, 83)( 14, 82)( 15, 84)( 16, 89)( 17, 88)( 18, 90)( 19,104)( 20,103)( 21,105)( 22,101)( 23,100)( 24,102)( 25,107)( 26,106)( 27,108)( 28, 95)( 29, 94)( 30, 96)( 31, 92)( 32, 91)( 33, 93)( 34, 98)( 35, 97)( 36, 99)( 37,131)( 38,130)( 39,132)( 40,128)( 41,127)( 42,129)( 43,134)( 44,133)( 45,135)( 46,140)( 47,139)( 48,141)( 49,137)( 50,136)( 51,138)( 52,143)( 53,142)( 54,144)( 55,113)( 56,112)( 57,114)( 58,110)( 59,109)( 60,111)( 61,116)( 62,115)( 63,117)( 64,122)( 65,121)( 66,123)( 67,119)( 68,118)( 69,120)( 70,125)( 71,124)( 72,126); s2 := Sym(144)!( 2, 3)( 5, 6)( 8, 9)( 11, 12)( 14, 15)( 17, 18)( 19, 28)( 20, 30)( 21, 29)( 22, 31)( 23, 33)( 24, 32)( 25, 34)( 26, 36)( 27, 35)( 37, 55)( 38, 57)( 39, 56)( 40, 58)( 41, 60)( 42, 59)( 43, 61)( 44, 63)( 45, 62)( 46, 64)( 47, 66)( 48, 65)( 49, 67)( 50, 69)( 51, 68)( 52, 70)( 53, 72)( 54, 71)( 73,109)( 74,111)( 75,110)( 76,112)( 77,114)( 78,113)( 79,115)( 80,117)( 81,116)( 82,118)( 83,120)( 84,119)( 85,121)( 86,123)( 87,122)( 88,124)( 89,126)( 90,125)( 91,136)( 92,138)( 93,137)( 94,139)( 95,141)( 96,140)( 97,142)( 98,144)( 99,143)(100,127)(101,129)(102,128)(103,130)(104,132)(105,131)(106,133)(107,135)(108,134); 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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*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*s0*s2*s1 >;
References
None.
to this polytope.