Overview
- Group
- SmallGroup(576,303)
- Rank
- 3
- Schläfli Type
- {36,4}
- Vertices, edges, …
- 72, 144, 8
- 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
- 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
Click an entry to reveal its facets and vertex figures.
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)( 38, 39)( 40, 44)( 41, 43)( 42, 45)( 47, 48)( 49, 53)( 50, 52)( 51, 54)( 55, 64)( 56, 66)( 57, 65)( 58, 71)( 59, 70)( 60, 72)( 61, 68)( 62, 67)( 63, 69)( 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)( 37,112)( 38,114)( 39,113)( 40,109)( 41,111)( 42,110)( 43,116)( 44,115)( 45,117)( 46,121)( 47,123)( 48,122)( 49,118)( 50,120)( 51,119)( 52,125)( 53,124)( 54,126)( 55,130)( 56,132)( 57,131)( 58,127)( 59,129)( 60,128)( 61,134)( 62,133)( 63,135)( 64,139)( 65,141)( 66,140)( 67,136)( 68,138)( 69,137)( 70,143)( 71,142)( 72,144);; 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*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 ];;
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)( 38, 39)( 40, 44)( 41, 43)( 42, 45)( 47, 48)( 49, 53)( 50, 52)( 51, 54)( 55, 64)( 56, 66)( 57, 65)( 58, 71)( 59, 70)( 60, 72)( 61, 68)( 62, 67)( 63, 69)( 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)( 37,112)( 38,114)( 39,113)( 40,109)( 41,111)( 42,110)( 43,116)( 44,115)( 45,117)( 46,121)( 47,123)( 48,122)( 49,118)( 50,120)( 51,119)( 52,125)( 53,124)( 54,126)( 55,130)( 56,132)( 57,131)( 58,127)( 59,129)( 60,128)( 61,134)( 62,133)( 63,135)( 64,139)( 65,141)( 66,140)( 67,136)( 68,138)( 69,137)( 70,143)( 71,142)( 72,144); 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*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 >;
References
None.
to this polytope.