Overview
- Group
- SmallGroup(1152,32532)
- Rank
- 3
- Schläfli Type
- {4,72}
- Vertices, edges, …
- 8, 288, 144
- Order of s0s1s2
- 36
- Order of s0s1s2s1
- 4
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
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
32-fold
36-fold
48-fold
72-fold
96-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.
Representations
Permutation Representation (GAP)
s0 := ( 37, 64)( 38, 65)( 39, 66)( 40, 67)( 41, 68)( 42, 69)( 43, 70)( 44, 71)( 45, 72)( 46, 55)( 47, 56)( 48, 57)( 49, 58)( 50, 59)( 51, 60)( 52, 61)( 53, 62)( 54, 63)(109,136)(110,137)(111,138)(112,139)(113,140)(114,141)(115,142)(116,143)(117,144)(118,127)(119,128)(120,129)(121,130)(122,131)(123,132)(124,133)(125,134)(126,135);; s1 := ( 2, 3)( 4, 9)( 5, 8)( 6, 7)( 11, 12)( 13, 18)( 14, 17)( 15, 16)( 19, 28)( 20, 30)( 21, 29)( 22, 36)( 23, 35)( 24, 34)( 25, 33)( 26, 32)( 27, 31)( 38, 39)( 40, 45)( 41, 44)( 42, 43)( 47, 48)( 49, 54)( 50, 53)( 51, 52)( 55, 64)( 56, 66)( 57, 65)( 58, 72)( 59, 71)( 60, 70)( 61, 69)( 62, 68)( 63, 67)( 73,109)( 74,111)( 75,110)( 76,117)( 77,116)( 78,115)( 79,114)( 80,113)( 81,112)( 82,118)( 83,120)( 84,119)( 85,126)( 86,125)( 87,124)( 88,123)( 89,122)( 90,121)( 91,136)( 92,138)( 93,137)( 94,144)( 95,143)( 96,142)( 97,141)( 98,140)( 99,139)(100,127)(101,129)(102,128)(103,135)(104,134)(105,133)(106,132)(107,131)(108,130);; s2 := ( 1, 76)( 2, 78)( 3, 77)( 4, 73)( 5, 75)( 6, 74)( 7, 81)( 8, 80)( 9, 79)( 10, 85)( 11, 87)( 12, 86)( 13, 82)( 14, 84)( 15, 83)( 16, 90)( 17, 89)( 18, 88)( 19, 94)( 20, 96)( 21, 95)( 22, 91)( 23, 93)( 24, 92)( 25, 99)( 26, 98)( 27, 97)( 28,103)( 29,105)( 30,104)( 31,100)( 32,102)( 33,101)( 34,108)( 35,107)( 36,106)( 37,139)( 38,141)( 39,140)( 40,136)( 41,138)( 42,137)( 43,144)( 44,143)( 45,142)( 46,130)( 47,132)( 48,131)( 49,127)( 50,129)( 51,128)( 52,135)( 53,134)( 54,133)( 55,121)( 56,123)( 57,122)( 58,118)( 59,120)( 60,119)( 61,126)( 62,125)( 63,124)( 64,112)( 65,114)( 66,113)( 67,109)( 68,111)( 69,110)( 70,117)( 71,116)( 72,115);; 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*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,
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*s0*s2*s1*s0*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*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(144)!( 37, 64)( 38, 65)( 39, 66)( 40, 67)( 41, 68)( 42, 69)( 43, 70)( 44, 71)( 45, 72)( 46, 55)( 47, 56)( 48, 57)( 49, 58)( 50, 59)( 51, 60)( 52, 61)( 53, 62)( 54, 63)(109,136)(110,137)(111,138)(112,139)(113,140)(114,141)(115,142)(116,143)(117,144)(118,127)(119,128)(120,129)(121,130)(122,131)(123,132)(124,133)(125,134)(126,135); s1 := Sym(144)!( 2, 3)( 4, 9)( 5, 8)( 6, 7)( 11, 12)( 13, 18)( 14, 17)( 15, 16)( 19, 28)( 20, 30)( 21, 29)( 22, 36)( 23, 35)( 24, 34)( 25, 33)( 26, 32)( 27, 31)( 38, 39)( 40, 45)( 41, 44)( 42, 43)( 47, 48)( 49, 54)( 50, 53)( 51, 52)( 55, 64)( 56, 66)( 57, 65)( 58, 72)( 59, 71)( 60, 70)( 61, 69)( 62, 68)( 63, 67)( 73,109)( 74,111)( 75,110)( 76,117)( 77,116)( 78,115)( 79,114)( 80,113)( 81,112)( 82,118)( 83,120)( 84,119)( 85,126)( 86,125)( 87,124)( 88,123)( 89,122)( 90,121)( 91,136)( 92,138)( 93,137)( 94,144)( 95,143)( 96,142)( 97,141)( 98,140)( 99,139)(100,127)(101,129)(102,128)(103,135)(104,134)(105,133)(106,132)(107,131)(108,130); s2 := Sym(144)!( 1, 76)( 2, 78)( 3, 77)( 4, 73)( 5, 75)( 6, 74)( 7, 81)( 8, 80)( 9, 79)( 10, 85)( 11, 87)( 12, 86)( 13, 82)( 14, 84)( 15, 83)( 16, 90)( 17, 89)( 18, 88)( 19, 94)( 20, 96)( 21, 95)( 22, 91)( 23, 93)( 24, 92)( 25, 99)( 26, 98)( 27, 97)( 28,103)( 29,105)( 30,104)( 31,100)( 32,102)( 33,101)( 34,108)( 35,107)( 36,106)( 37,139)( 38,141)( 39,140)( 40,136)( 41,138)( 42,137)( 43,144)( 44,143)( 45,142)( 46,130)( 47,132)( 48,131)( 49,127)( 50,129)( 51,128)( 52,135)( 53,134)( 54,133)( 55,121)( 56,123)( 57,122)( 58,118)( 59,120)( 60,119)( 61,126)( 62,125)( 63,124)( 64,112)( 65,114)( 66,113)( 67,109)( 68,111)( 69,110)( 70,117)( 71,116)( 72,115); 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*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, 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*s0*s2*s1*s0*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*s0*s1 >;
References
None.
to this polytope.