Overview
- Group
- SmallGroup(1200,1002)
- Rank
- 3
- Schläfli Type
- {10,12}
- Vertices, edges, …
- 50, 300, 60
- Order of s0s1s2
- 12
- Order of s0s1s2s1
- 10
- 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
6-fold
25-fold
50-fold
75-fold
100-fold
150-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 := ( 1, 76)( 2, 80)( 3, 79)( 4, 78)( 5, 77)( 6, 96)( 7,100)( 8, 99)( 9, 98)( 10, 97)( 11, 91)( 12, 95)( 13, 94)( 14, 93)( 15, 92)( 16, 86)( 17, 90)( 18, 89)( 19, 88)( 20, 87)( 21, 81)( 22, 85)( 23, 84)( 24, 83)( 25, 82)( 26,101)( 27,105)( 28,104)( 29,103)( 30,102)( 31,121)( 32,125)( 33,124)( 34,123)( 35,122)( 36,116)( 37,120)( 38,119)( 39,118)( 40,117)( 41,111)( 42,115)( 43,114)( 44,113)( 45,112)( 46,106)( 47,110)( 48,109)( 49,108)( 50,107)( 51,126)( 52,130)( 53,129)( 54,128)( 55,127)( 56,146)( 57,150)( 58,149)( 59,148)( 60,147)( 61,141)( 62,145)( 63,144)( 64,143)( 65,142)( 66,136)( 67,140)( 68,139)( 69,138)( 70,137)( 71,131)( 72,135)( 73,134)( 74,133)( 75,132);; s1 := ( 1, 6)( 2, 17)( 4, 14)( 5, 25)( 7, 12)( 8, 23)( 10, 20)( 11, 21)( 13, 18)( 19, 24)( 26, 56)( 27, 67)( 28, 53)( 29, 64)( 30, 75)( 31, 51)( 32, 62)( 33, 73)( 34, 59)( 35, 70)( 36, 71)( 37, 57)( 38, 68)( 39, 54)( 40, 65)( 41, 66)( 42, 52)( 43, 63)( 44, 74)( 45, 60)( 46, 61)( 47, 72)( 48, 58)( 49, 69)( 50, 55)( 76, 81)( 77, 92)( 79, 89)( 80,100)( 82, 87)( 83, 98)( 85, 95)( 86, 96)( 88, 93)( 94, 99)(101,131)(102,142)(103,128)(104,139)(105,150)(106,126)(107,137)(108,148)(109,134)(110,145)(111,146)(112,132)(113,143)(114,129)(115,140)(116,141)(117,127)(118,138)(119,149)(120,135)(121,136)(122,147)(123,133)(124,144)(125,130);; s2 := ( 1, 26)( 2, 34)( 3, 37)( 4, 45)( 5, 48)( 6, 38)( 7, 41)( 8, 49)( 9, 27)( 10, 35)( 11, 50)( 12, 28)( 13, 31)( 14, 39)( 15, 42)( 16, 32)( 17, 40)( 18, 43)( 19, 46)( 20, 29)( 21, 44)( 22, 47)( 23, 30)( 24, 33)( 25, 36)( 52, 59)( 53, 62)( 54, 70)( 55, 73)( 56, 63)( 57, 66)( 58, 74)( 61, 75)( 65, 67)( 69, 71)( 76,101)( 77,109)( 78,112)( 79,120)( 80,123)( 81,113)( 82,116)( 83,124)( 84,102)( 85,110)( 86,125)( 87,103)( 88,106)( 89,114)( 90,117)( 91,107)( 92,115)( 93,118)( 94,121)( 95,104)( 96,119)( 97,122)( 98,105)( 99,108)(100,111)(127,134)(128,137)(129,145)(130,148)(131,138)(132,141)(133,149)(136,150)(140,142)(144,146);; 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*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(150)!( 1, 76)( 2, 80)( 3, 79)( 4, 78)( 5, 77)( 6, 96)( 7,100)( 8, 99)( 9, 98)( 10, 97)( 11, 91)( 12, 95)( 13, 94)( 14, 93)( 15, 92)( 16, 86)( 17, 90)( 18, 89)( 19, 88)( 20, 87)( 21, 81)( 22, 85)( 23, 84)( 24, 83)( 25, 82)( 26,101)( 27,105)( 28,104)( 29,103)( 30,102)( 31,121)( 32,125)( 33,124)( 34,123)( 35,122)( 36,116)( 37,120)( 38,119)( 39,118)( 40,117)( 41,111)( 42,115)( 43,114)( 44,113)( 45,112)( 46,106)( 47,110)( 48,109)( 49,108)( 50,107)( 51,126)( 52,130)( 53,129)( 54,128)( 55,127)( 56,146)( 57,150)( 58,149)( 59,148)( 60,147)( 61,141)( 62,145)( 63,144)( 64,143)( 65,142)( 66,136)( 67,140)( 68,139)( 69,138)( 70,137)( 71,131)( 72,135)( 73,134)( 74,133)( 75,132); s1 := Sym(150)!( 1, 6)( 2, 17)( 4, 14)( 5, 25)( 7, 12)( 8, 23)( 10, 20)( 11, 21)( 13, 18)( 19, 24)( 26, 56)( 27, 67)( 28, 53)( 29, 64)( 30, 75)( 31, 51)( 32, 62)( 33, 73)( 34, 59)( 35, 70)( 36, 71)( 37, 57)( 38, 68)( 39, 54)( 40, 65)( 41, 66)( 42, 52)( 43, 63)( 44, 74)( 45, 60)( 46, 61)( 47, 72)( 48, 58)( 49, 69)( 50, 55)( 76, 81)( 77, 92)( 79, 89)( 80,100)( 82, 87)( 83, 98)( 85, 95)( 86, 96)( 88, 93)( 94, 99)(101,131)(102,142)(103,128)(104,139)(105,150)(106,126)(107,137)(108,148)(109,134)(110,145)(111,146)(112,132)(113,143)(114,129)(115,140)(116,141)(117,127)(118,138)(119,149)(120,135)(121,136)(122,147)(123,133)(124,144)(125,130); s2 := Sym(150)!( 1, 26)( 2, 34)( 3, 37)( 4, 45)( 5, 48)( 6, 38)( 7, 41)( 8, 49)( 9, 27)( 10, 35)( 11, 50)( 12, 28)( 13, 31)( 14, 39)( 15, 42)( 16, 32)( 17, 40)( 18, 43)( 19, 46)( 20, 29)( 21, 44)( 22, 47)( 23, 30)( 24, 33)( 25, 36)( 52, 59)( 53, 62)( 54, 70)( 55, 73)( 56, 63)( 57, 66)( 58, 74)( 61, 75)( 65, 67)( 69, 71)( 76,101)( 77,109)( 78,112)( 79,120)( 80,123)( 81,113)( 82,116)( 83,124)( 84,102)( 85,110)( 86,125)( 87,103)( 88,106)( 89,114)( 90,117)( 91,107)( 92,115)( 93,118)( 94,121)( 95,104)( 96,119)( 97,122)( 98,105)( 99,108)(100,111)(127,134)(128,137)(129,145)(130,148)(131,138)(132,141)(133,149)(136,150)(140,142)(144,146); poly := sub<Sym(150)|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*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.