Overview
- Group
- SmallGroup(1248,1329)
- Rank
- 4
- Schläfli Type
- {26,6,4}
- Vertices, edges, …
- 26, 78, 12, 4
- Order of s0s1s2s3
- 156
- Order of s0s1s2s3s2s1
- 2
- Also known as
- {{26,6|2},{6,4|2}}. if this polytope has another name.
Special Properties
- Universal
- 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
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 13)( 3, 12)( 4, 11)( 5, 10)( 6, 9)( 7, 8)( 15, 26)( 16, 25)( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 28, 39)( 29, 38)( 30, 37)( 31, 36)( 32, 35)( 33, 34)( 41, 52)( 42, 51)( 43, 50)( 44, 49)( 45, 48)( 46, 47)( 54, 65)( 55, 64)( 56, 63)( 57, 62)( 58, 61)( 59, 60)( 67, 78)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 80, 91)( 81, 90)( 82, 89)( 83, 88)( 84, 87)( 85, 86)( 93,104)( 94,103)( 95,102)( 96,101)( 97,100)( 98, 99)(106,117)(107,116)(108,115)(109,114)(110,113)(111,112)(119,130)(120,129)(121,128)(122,127)(123,126)(124,125)(132,143)(133,142)(134,141)(135,140)(136,139)(137,138)(145,156)(146,155)(147,154)(148,153)(149,152)(150,151);; s1 := ( 1, 2)( 3, 13)( 4, 12)( 5, 11)( 6, 10)( 7, 9)( 14, 28)( 15, 27)( 16, 39)( 17, 38)( 18, 37)( 19, 36)( 20, 35)( 21, 34)( 22, 33)( 23, 32)( 24, 31)( 25, 30)( 26, 29)( 40, 41)( 42, 52)( 43, 51)( 44, 50)( 45, 49)( 46, 48)( 53, 67)( 54, 66)( 55, 78)( 56, 77)( 57, 76)( 58, 75)( 59, 74)( 60, 73)( 61, 72)( 62, 71)( 63, 70)( 64, 69)( 65, 68)( 79, 80)( 81, 91)( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 92,106)( 93,105)( 94,117)( 95,116)( 96,115)( 97,114)( 98,113)( 99,112)(100,111)(101,110)(102,109)(103,108)(104,107)(118,119)(120,130)(121,129)(122,128)(123,127)(124,126)(131,145)(132,144)(133,156)(134,155)(135,154)(136,153)(137,152)(138,151)(139,150)(140,149)(141,148)(142,147)(143,146);; s2 := ( 1, 14)( 2, 15)( 3, 16)( 4, 17)( 5, 18)( 6, 19)( 7, 20)( 8, 21)( 9, 22)( 10, 23)( 11, 24)( 12, 25)( 13, 26)( 40, 53)( 41, 54)( 42, 55)( 43, 56)( 44, 57)( 45, 58)( 46, 59)( 47, 60)( 48, 61)( 49, 62)( 50, 63)( 51, 64)( 52, 65)( 79,131)( 80,132)( 81,133)( 82,134)( 83,135)( 84,136)( 85,137)( 86,138)( 87,139)( 88,140)( 89,141)( 90,142)( 91,143)( 92,118)( 93,119)( 94,120)( 95,121)( 96,122)( 97,123)( 98,124)( 99,125)(100,126)(101,127)(102,128)(103,129)(104,130)(105,144)(106,145)(107,146)(108,147)(109,148)(110,149)(111,150)(112,151)(113,152)(114,153)(115,154)(116,155)(117,156);; s3 := ( 1, 79)( 2, 80)( 3, 81)( 4, 82)( 5, 83)( 6, 84)( 7, 85)( 8, 86)( 9, 87)( 10, 88)( 11, 89)( 12, 90)( 13, 91)( 14, 92)( 15, 93)( 16, 94)( 17, 95)( 18, 96)( 19, 97)( 20, 98)( 21, 99)( 22,100)( 23,101)( 24,102)( 25,103)( 26,104)( 27,105)( 28,106)( 29,107)( 30,108)( 31,109)( 32,110)( 33,111)( 34,112)( 35,113)( 36,114)( 37,115)( 38,116)( 39,117)( 40,118)( 41,119)( 42,120)( 43,121)( 44,122)( 45,123)( 46,124)( 47,125)( 48,126)( 49,127)( 50,128)( 51,129)( 52,130)( 53,131)( 54,132)( 55,133)( 56,134)( 57,135)( 58,136)( 59,137)( 60,138)( 61,139)( 62,140)( 63,141)( 64,142)( 65,143)( 66,144)( 67,145)( 68,146)( 69,147)( 70,148)( 71,149)( 72,150)( 73,151)( 74,152)( 75,153)( 76,154)( 77,155)( 78,156);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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(156)!( 2, 13)( 3, 12)( 4, 11)( 5, 10)( 6, 9)( 7, 8)( 15, 26)( 16, 25)( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 28, 39)( 29, 38)( 30, 37)( 31, 36)( 32, 35)( 33, 34)( 41, 52)( 42, 51)( 43, 50)( 44, 49)( 45, 48)( 46, 47)( 54, 65)( 55, 64)( 56, 63)( 57, 62)( 58, 61)( 59, 60)( 67, 78)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 80, 91)( 81, 90)( 82, 89)( 83, 88)( 84, 87)( 85, 86)( 93,104)( 94,103)( 95,102)( 96,101)( 97,100)( 98, 99)(106,117)(107,116)(108,115)(109,114)(110,113)(111,112)(119,130)(120,129)(121,128)(122,127)(123,126)(124,125)(132,143)(133,142)(134,141)(135,140)(136,139)(137,138)(145,156)(146,155)(147,154)(148,153)(149,152)(150,151); s1 := Sym(156)!( 1, 2)( 3, 13)( 4, 12)( 5, 11)( 6, 10)( 7, 9)( 14, 28)( 15, 27)( 16, 39)( 17, 38)( 18, 37)( 19, 36)( 20, 35)( 21, 34)( 22, 33)( 23, 32)( 24, 31)( 25, 30)( 26, 29)( 40, 41)( 42, 52)( 43, 51)( 44, 50)( 45, 49)( 46, 48)( 53, 67)( 54, 66)( 55, 78)( 56, 77)( 57, 76)( 58, 75)( 59, 74)( 60, 73)( 61, 72)( 62, 71)( 63, 70)( 64, 69)( 65, 68)( 79, 80)( 81, 91)( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 92,106)( 93,105)( 94,117)( 95,116)( 96,115)( 97,114)( 98,113)( 99,112)(100,111)(101,110)(102,109)(103,108)(104,107)(118,119)(120,130)(121,129)(122,128)(123,127)(124,126)(131,145)(132,144)(133,156)(134,155)(135,154)(136,153)(137,152)(138,151)(139,150)(140,149)(141,148)(142,147)(143,146); s2 := Sym(156)!( 1, 14)( 2, 15)( 3, 16)( 4, 17)( 5, 18)( 6, 19)( 7, 20)( 8, 21)( 9, 22)( 10, 23)( 11, 24)( 12, 25)( 13, 26)( 40, 53)( 41, 54)( 42, 55)( 43, 56)( 44, 57)( 45, 58)( 46, 59)( 47, 60)( 48, 61)( 49, 62)( 50, 63)( 51, 64)( 52, 65)( 79,131)( 80,132)( 81,133)( 82,134)( 83,135)( 84,136)( 85,137)( 86,138)( 87,139)( 88,140)( 89,141)( 90,142)( 91,143)( 92,118)( 93,119)( 94,120)( 95,121)( 96,122)( 97,123)( 98,124)( 99,125)(100,126)(101,127)(102,128)(103,129)(104,130)(105,144)(106,145)(107,146)(108,147)(109,148)(110,149)(111,150)(112,151)(113,152)(114,153)(115,154)(116,155)(117,156); s3 := Sym(156)!( 1, 79)( 2, 80)( 3, 81)( 4, 82)( 5, 83)( 6, 84)( 7, 85)( 8, 86)( 9, 87)( 10, 88)( 11, 89)( 12, 90)( 13, 91)( 14, 92)( 15, 93)( 16, 94)( 17, 95)( 18, 96)( 19, 97)( 20, 98)( 21, 99)( 22,100)( 23,101)( 24,102)( 25,103)( 26,104)( 27,105)( 28,106)( 29,107)( 30,108)( 31,109)( 32,110)( 33,111)( 34,112)( 35,113)( 36,114)( 37,115)( 38,116)( 39,117)( 40,118)( 41,119)( 42,120)( 43,121)( 44,122)( 45,123)( 46,124)( 47,125)( 48,126)( 49,127)( 50,128)( 51,129)( 52,130)( 53,131)( 54,132)( 55,133)( 56,134)( 57,135)( 58,136)( 59,137)( 60,138)( 61,139)( 62,140)( 63,141)( 64,142)( 65,143)( 66,144)( 67,145)( 68,146)( 69,147)( 70,148)( 71,149)( 72,150)( 73,151)( 74,152)( 75,153)( 76,154)( 77,155)( 78,156); poly := sub<Sym(156)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 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.