Overview
- Group
- SmallGroup(576,309)
- Rank
- 3
- Schläfli Type
- {72,4}
- Vertices, edges, …
- 72, 144, 4
- Order of s0s1s2
- 72
- Order of s0s1s2s1
- 4
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
- Self-Petrie
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, 8)( 5, 7)( 6, 9)( 11, 12)( 13, 17)( 14, 16)( 15, 18)( 19, 28)( 20, 30)( 21, 29)( 22, 35)( 23, 34)( 24, 36)( 25, 32)( 26, 31)( 27, 33)( 37, 46)( 38, 48)( 39, 47)( 40, 53)( 41, 52)( 42, 54)( 43, 50)( 44, 49)( 45, 51)( 56, 57)( 58, 62)( 59, 61)( 60, 63)( 65, 66)( 67, 71)( 68, 70)( 69, 72)( 73,109)( 74,111)( 75,110)( 76,116)( 77,115)( 78,117)( 79,113)( 80,112)( 81,114)( 82,118)( 83,120)( 84,119)( 85,125)( 86,124)( 87,126)( 88,122)( 89,121)( 90,123)( 91,136)( 92,138)( 93,137)( 94,143)( 95,142)( 96,144)( 97,140)( 98,139)( 99,141)(100,127)(101,129)(102,128)(103,134)(104,133)(105,135)(106,131)(107,130)(108,132);; s1 := ( 1, 76)( 2, 78)( 3, 77)( 4, 73)( 5, 75)( 6, 74)( 7, 80)( 8, 79)( 9, 81)( 10, 85)( 11, 87)( 12, 86)( 13, 82)( 14, 84)( 15, 83)( 16, 89)( 17, 88)( 18, 90)( 19, 94)( 20, 96)( 21, 95)( 22, 91)( 23, 93)( 24, 92)( 25, 98)( 26, 97)( 27, 99)( 28,103)( 29,105)( 30,104)( 31,100)( 32,102)( 33,101)( 34,107)( 35,106)( 36,108)( 37,121)( 38,123)( 39,122)( 40,118)( 41,120)( 42,119)( 43,125)( 44,124)( 45,126)( 46,112)( 47,114)( 48,113)( 49,109)( 50,111)( 51,110)( 52,116)( 53,115)( 54,117)( 55,139)( 56,141)( 57,140)( 58,136)( 59,138)( 60,137)( 61,143)( 62,142)( 63,144)( 64,130)( 65,132)( 66,131)( 67,127)( 68,129)( 69,128)( 70,134)( 71,133)( 72,135);; s2 := ( 37, 46)( 38, 47)( 39, 48)( 40, 49)( 41, 50)( 42, 51)( 43, 52)( 44, 53)( 45, 54)( 55, 64)( 56, 65)( 57, 66)( 58, 67)( 59, 68)( 60, 69)( 61, 70)( 62, 71)( 63, 72)( 73, 91)( 74, 92)( 75, 93)( 76, 94)( 77, 95)( 78, 96)( 79, 97)( 80, 98)( 81, 99)( 82,100)( 83,101)( 84,102)( 85,103)( 86,104)( 87,105)( 88,106)( 89,107)( 90,108)(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);; 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,
s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*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*s2*s1*s0*s1*s0*s2*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(144)!( 2, 3)( 4, 8)( 5, 7)( 6, 9)( 11, 12)( 13, 17)( 14, 16)( 15, 18)( 19, 28)( 20, 30)( 21, 29)( 22, 35)( 23, 34)( 24, 36)( 25, 32)( 26, 31)( 27, 33)( 37, 46)( 38, 48)( 39, 47)( 40, 53)( 41, 52)( 42, 54)( 43, 50)( 44, 49)( 45, 51)( 56, 57)( 58, 62)( 59, 61)( 60, 63)( 65, 66)( 67, 71)( 68, 70)( 69, 72)( 73,109)( 74,111)( 75,110)( 76,116)( 77,115)( 78,117)( 79,113)( 80,112)( 81,114)( 82,118)( 83,120)( 84,119)( 85,125)( 86,124)( 87,126)( 88,122)( 89,121)( 90,123)( 91,136)( 92,138)( 93,137)( 94,143)( 95,142)( 96,144)( 97,140)( 98,139)( 99,141)(100,127)(101,129)(102,128)(103,134)(104,133)(105,135)(106,131)(107,130)(108,132); s1 := Sym(144)!( 1, 76)( 2, 78)( 3, 77)( 4, 73)( 5, 75)( 6, 74)( 7, 80)( 8, 79)( 9, 81)( 10, 85)( 11, 87)( 12, 86)( 13, 82)( 14, 84)( 15, 83)( 16, 89)( 17, 88)( 18, 90)( 19, 94)( 20, 96)( 21, 95)( 22, 91)( 23, 93)( 24, 92)( 25, 98)( 26, 97)( 27, 99)( 28,103)( 29,105)( 30,104)( 31,100)( 32,102)( 33,101)( 34,107)( 35,106)( 36,108)( 37,121)( 38,123)( 39,122)( 40,118)( 41,120)( 42,119)( 43,125)( 44,124)( 45,126)( 46,112)( 47,114)( 48,113)( 49,109)( 50,111)( 51,110)( 52,116)( 53,115)( 54,117)( 55,139)( 56,141)( 57,140)( 58,136)( 59,138)( 60,137)( 61,143)( 62,142)( 63,144)( 64,130)( 65,132)( 66,131)( 67,127)( 68,129)( 69,128)( 70,134)( 71,133)( 72,135); s2 := Sym(144)!( 37, 46)( 38, 47)( 39, 48)( 40, 49)( 41, 50)( 42, 51)( 43, 52)( 44, 53)( 45, 54)( 55, 64)( 56, 65)( 57, 66)( 58, 67)( 59, 68)( 60, 69)( 61, 70)( 62, 71)( 63, 72)( 73, 91)( 74, 92)( 75, 93)( 76, 94)( 77, 95)( 78, 96)( 79, 97)( 80, 98)( 81, 99)( 82,100)( 83,101)( 84,102)( 85,103)( 86,104)( 87,105)( 88,106)( 89,107)( 90,108)(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); 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, s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*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*s2*s1*s0*s1*s0*s2*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.