Overview
- Group
- SmallGroup(624,178)
- Rank
- 3
- Schläfli Type
- {12,26}
- Vertices, edges, …
- 12, 156, 26
- Order of s0s1s2
- 156
- Order of s0s1s2s1
- 2
- Also known as
- {12,26|2}. if this polytope has another name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
6-fold
12-fold
13-fold
26-fold
39-fold
52-fold
78-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 := ( 14, 27)( 15, 28)( 16, 29)( 17, 30)( 18, 31)( 19, 32)( 20, 33)( 21, 34)( 22, 35)( 23, 36)( 24, 37)( 25, 38)( 26, 39)( 53, 66)( 54, 67)( 55, 68)( 56, 69)( 57, 70)( 58, 71)( 59, 72)( 60, 73)( 61, 74)( 62, 75)( 63, 76)( 64, 77)( 65, 78)( 79,118)( 80,119)( 81,120)( 82,121)( 83,122)( 84,123)( 85,124)( 86,125)( 87,126)( 88,127)( 89,128)( 90,129)( 91,130)( 92,144)( 93,145)( 94,146)( 95,147)( 96,148)( 97,149)( 98,150)( 99,151)(100,152)(101,153)(102,154)(103,155)(104,156)(105,131)(106,132)(107,133)(108,134)(109,135)(110,136)(111,137)(112,138)(113,139)(114,140)(115,141)(116,142)(117,143);; s1 := ( 1, 92)( 2,104)( 3,103)( 4,102)( 5,101)( 6,100)( 7, 99)( 8, 98)( 9, 97)( 10, 96)( 11, 95)( 12, 94)( 13, 93)( 14, 79)( 15, 91)( 16, 90)( 17, 89)( 18, 88)( 19, 87)( 20, 86)( 21, 85)( 22, 84)( 23, 83)( 24, 82)( 25, 81)( 26, 80)( 27,105)( 28,117)( 29,116)( 30,115)( 31,114)( 32,113)( 33,112)( 34,111)( 35,110)( 36,109)( 37,108)( 38,107)( 39,106)( 40,131)( 41,143)( 42,142)( 43,141)( 44,140)( 45,139)( 46,138)( 47,137)( 48,136)( 49,135)( 50,134)( 51,133)( 52,132)( 53,118)( 54,130)( 55,129)( 56,128)( 57,127)( 58,126)( 59,125)( 60,124)( 61,123)( 62,122)( 63,121)( 64,120)( 65,119)( 66,144)( 67,156)( 68,155)( 69,154)( 70,153)( 71,152)( 72,151)( 73,150)( 74,149)( 75,148)( 76,147)( 77,146)( 78,145);; s2 := ( 1, 2)( 3, 13)( 4, 12)( 5, 11)( 6, 10)( 7, 9)( 14, 15)( 16, 26)( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 28)( 29, 39)( 30, 38)( 31, 37)( 32, 36)( 33, 35)( 40, 41)( 42, 52)( 43, 51)( 44, 50)( 45, 49)( 46, 48)( 53, 54)( 55, 65)( 56, 64)( 57, 63)( 58, 62)( 59, 61)( 66, 67)( 68, 78)( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 79, 80)( 81, 91)( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 92, 93)( 94,104)( 95,103)( 96,102)( 97,101)( 98,100)(105,106)(107,117)(108,116)(109,115)(110,114)(111,113)(118,119)(120,130)(121,129)(122,128)(123,127)(124,126)(131,132)(133,143)(134,142)(135,141)(136,140)(137,139)(144,145)(146,156)(147,155)(148,154)(149,153)(150,152);; 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*s0*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,
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*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(156)!( 14, 27)( 15, 28)( 16, 29)( 17, 30)( 18, 31)( 19, 32)( 20, 33)( 21, 34)( 22, 35)( 23, 36)( 24, 37)( 25, 38)( 26, 39)( 53, 66)( 54, 67)( 55, 68)( 56, 69)( 57, 70)( 58, 71)( 59, 72)( 60, 73)( 61, 74)( 62, 75)( 63, 76)( 64, 77)( 65, 78)( 79,118)( 80,119)( 81,120)( 82,121)( 83,122)( 84,123)( 85,124)( 86,125)( 87,126)( 88,127)( 89,128)( 90,129)( 91,130)( 92,144)( 93,145)( 94,146)( 95,147)( 96,148)( 97,149)( 98,150)( 99,151)(100,152)(101,153)(102,154)(103,155)(104,156)(105,131)(106,132)(107,133)(108,134)(109,135)(110,136)(111,137)(112,138)(113,139)(114,140)(115,141)(116,142)(117,143); s1 := Sym(156)!( 1, 92)( 2,104)( 3,103)( 4,102)( 5,101)( 6,100)( 7, 99)( 8, 98)( 9, 97)( 10, 96)( 11, 95)( 12, 94)( 13, 93)( 14, 79)( 15, 91)( 16, 90)( 17, 89)( 18, 88)( 19, 87)( 20, 86)( 21, 85)( 22, 84)( 23, 83)( 24, 82)( 25, 81)( 26, 80)( 27,105)( 28,117)( 29,116)( 30,115)( 31,114)( 32,113)( 33,112)( 34,111)( 35,110)( 36,109)( 37,108)( 38,107)( 39,106)( 40,131)( 41,143)( 42,142)( 43,141)( 44,140)( 45,139)( 46,138)( 47,137)( 48,136)( 49,135)( 50,134)( 51,133)( 52,132)( 53,118)( 54,130)( 55,129)( 56,128)( 57,127)( 58,126)( 59,125)( 60,124)( 61,123)( 62,122)( 63,121)( 64,120)( 65,119)( 66,144)( 67,156)( 68,155)( 69,154)( 70,153)( 71,152)( 72,151)( 73,150)( 74,149)( 75,148)( 76,147)( 77,146)( 78,145); s2 := Sym(156)!( 1, 2)( 3, 13)( 4, 12)( 5, 11)( 6, 10)( 7, 9)( 14, 15)( 16, 26)( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 28)( 29, 39)( 30, 38)( 31, 37)( 32, 36)( 33, 35)( 40, 41)( 42, 52)( 43, 51)( 44, 50)( 45, 49)( 46, 48)( 53, 54)( 55, 65)( 56, 64)( 57, 63)( 58, 62)( 59, 61)( 66, 67)( 68, 78)( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 79, 80)( 81, 91)( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 92, 93)( 94,104)( 95,103)( 96,102)( 97,101)( 98,100)(105,106)(107,117)(108,116)(109,115)(110,114)(111,113)(118,119)(120,130)(121,129)(122,128)(123,127)(124,126)(131,132)(133,143)(134,142)(135,141)(136,140)(137,139)(144,145)(146,156)(147,155)(148,154)(149,153)(150,152); poly := sub<Sym(156)|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*s0*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, 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*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.