Overview
- Group
- SmallGroup(768,145174)
- Rank
- 4
- Schläfli Type
- {2,24,8}
- Vertices, edges, …
- 2, 24, 96, 8
- Order of s0s1s2s3
- 24
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
8-fold
12-fold
16-fold
24-fold
32-fold
48-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 3, 99)( 4,101)( 5,100)( 6,102)( 7,104)( 8,103)( 9,105)( 10,107)( 11,106)( 12,108)( 13,110)( 14,109)( 15,114)( 16,116)( 17,115)( 18,111)( 19,113)( 20,112)( 21,120)( 22,122)( 23,121)( 24,117)( 25,119)( 26,118)( 27,129)( 28,131)( 29,130)( 30,132)( 31,134)( 32,133)( 33,123)( 34,125)( 35,124)( 36,126)( 37,128)( 38,127)( 39,144)( 40,146)( 41,145)( 42,141)( 43,143)( 44,142)( 45,138)( 46,140)( 47,139)( 48,135)( 49,137)( 50,136)( 51,147)( 52,149)( 53,148)( 54,150)( 55,152)( 56,151)( 57,153)( 58,155)( 59,154)( 60,156)( 61,158)( 62,157)( 63,162)( 64,164)( 65,163)( 66,159)( 67,161)( 68,160)( 69,168)( 70,170)( 71,169)( 72,165)( 73,167)( 74,166)( 75,177)( 76,179)( 77,178)( 78,180)( 79,182)( 80,181)( 81,171)( 82,173)( 83,172)( 84,174)( 85,176)( 86,175)( 87,192)( 88,194)( 89,193)( 90,189)( 91,191)( 92,190)( 93,186)( 94,188)( 95,187)( 96,183)( 97,185)( 98,184);; s2 := ( 3, 4)( 6, 7)( 9, 10)( 12, 13)( 15, 19)( 16, 18)( 17, 20)( 21, 25)( 22, 24)( 23, 26)( 27, 34)( 28, 33)( 29, 35)( 30, 37)( 31, 36)( 32, 38)( 39, 49)( 40, 48)( 41, 50)( 42, 46)( 43, 45)( 44, 47)( 51, 64)( 52, 63)( 53, 65)( 54, 67)( 55, 66)( 56, 68)( 57, 70)( 58, 69)( 59, 71)( 60, 73)( 61, 72)( 62, 74)( 75, 94)( 76, 93)( 77, 95)( 78, 97)( 79, 96)( 80, 98)( 81, 88)( 82, 87)( 83, 89)( 84, 91)( 85, 90)( 86, 92)( 99,124)(100,123)(101,125)(102,127)(103,126)(104,128)(105,130)(106,129)(107,131)(108,133)(109,132)(110,134)(111,139)(112,138)(113,140)(114,136)(115,135)(116,137)(117,145)(118,144)(119,146)(120,142)(121,141)(122,143)(147,187)(148,186)(149,188)(150,184)(151,183)(152,185)(153,193)(154,192)(155,194)(156,190)(157,189)(158,191)(159,175)(160,174)(161,176)(162,172)(163,171)(164,173)(165,181)(166,180)(167,182)(168,178)(169,177)(170,179);; s3 := ( 3, 51)( 4, 52)( 5, 53)( 6, 54)( 7, 55)( 8, 56)( 9, 57)( 10, 58)( 11, 59)( 12, 60)( 13, 61)( 14, 62)( 15, 66)( 16, 67)( 17, 68)( 18, 63)( 19, 64)( 20, 65)( 21, 72)( 22, 73)( 23, 74)( 24, 69)( 25, 70)( 26, 71)( 27, 78)( 28, 79)( 29, 80)( 30, 75)( 31, 76)( 32, 77)( 33, 84)( 34, 85)( 35, 86)( 36, 81)( 37, 82)( 38, 83)( 39, 87)( 40, 88)( 41, 89)( 42, 90)( 43, 91)( 44, 92)( 45, 93)( 46, 94)( 47, 95)( 48, 96)( 49, 97)( 50, 98)( 99,147)(100,148)(101,149)(102,150)(103,151)(104,152)(105,153)(106,154)(107,155)(108,156)(109,157)(110,158)(111,162)(112,163)(113,164)(114,159)(115,160)(116,161)(117,168)(118,169)(119,170)(120,165)(121,166)(122,167)(123,174)(124,175)(125,176)(126,171)(127,172)(128,173)(129,180)(130,181)(131,182)(132,177)(133,178)(134,179)(135,183)(136,184)(137,185)(138,186)(139,187)(140,188)(141,189)(142,190)(143,191)(144,192)(145,193)(146,194);; 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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*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(194)!(1,2); s1 := Sym(194)!( 3, 99)( 4,101)( 5,100)( 6,102)( 7,104)( 8,103)( 9,105)( 10,107)( 11,106)( 12,108)( 13,110)( 14,109)( 15,114)( 16,116)( 17,115)( 18,111)( 19,113)( 20,112)( 21,120)( 22,122)( 23,121)( 24,117)( 25,119)( 26,118)( 27,129)( 28,131)( 29,130)( 30,132)( 31,134)( 32,133)( 33,123)( 34,125)( 35,124)( 36,126)( 37,128)( 38,127)( 39,144)( 40,146)( 41,145)( 42,141)( 43,143)( 44,142)( 45,138)( 46,140)( 47,139)( 48,135)( 49,137)( 50,136)( 51,147)( 52,149)( 53,148)( 54,150)( 55,152)( 56,151)( 57,153)( 58,155)( 59,154)( 60,156)( 61,158)( 62,157)( 63,162)( 64,164)( 65,163)( 66,159)( 67,161)( 68,160)( 69,168)( 70,170)( 71,169)( 72,165)( 73,167)( 74,166)( 75,177)( 76,179)( 77,178)( 78,180)( 79,182)( 80,181)( 81,171)( 82,173)( 83,172)( 84,174)( 85,176)( 86,175)( 87,192)( 88,194)( 89,193)( 90,189)( 91,191)( 92,190)( 93,186)( 94,188)( 95,187)( 96,183)( 97,185)( 98,184); s2 := Sym(194)!( 3, 4)( 6, 7)( 9, 10)( 12, 13)( 15, 19)( 16, 18)( 17, 20)( 21, 25)( 22, 24)( 23, 26)( 27, 34)( 28, 33)( 29, 35)( 30, 37)( 31, 36)( 32, 38)( 39, 49)( 40, 48)( 41, 50)( 42, 46)( 43, 45)( 44, 47)( 51, 64)( 52, 63)( 53, 65)( 54, 67)( 55, 66)( 56, 68)( 57, 70)( 58, 69)( 59, 71)( 60, 73)( 61, 72)( 62, 74)( 75, 94)( 76, 93)( 77, 95)( 78, 97)( 79, 96)( 80, 98)( 81, 88)( 82, 87)( 83, 89)( 84, 91)( 85, 90)( 86, 92)( 99,124)(100,123)(101,125)(102,127)(103,126)(104,128)(105,130)(106,129)(107,131)(108,133)(109,132)(110,134)(111,139)(112,138)(113,140)(114,136)(115,135)(116,137)(117,145)(118,144)(119,146)(120,142)(121,141)(122,143)(147,187)(148,186)(149,188)(150,184)(151,183)(152,185)(153,193)(154,192)(155,194)(156,190)(157,189)(158,191)(159,175)(160,174)(161,176)(162,172)(163,171)(164,173)(165,181)(166,180)(167,182)(168,178)(169,177)(170,179); s3 := Sym(194)!( 3, 51)( 4, 52)( 5, 53)( 6, 54)( 7, 55)( 8, 56)( 9, 57)( 10, 58)( 11, 59)( 12, 60)( 13, 61)( 14, 62)( 15, 66)( 16, 67)( 17, 68)( 18, 63)( 19, 64)( 20, 65)( 21, 72)( 22, 73)( 23, 74)( 24, 69)( 25, 70)( 26, 71)( 27, 78)( 28, 79)( 29, 80)( 30, 75)( 31, 76)( 32, 77)( 33, 84)( 34, 85)( 35, 86)( 36, 81)( 37, 82)( 38, 83)( 39, 87)( 40, 88)( 41, 89)( 42, 90)( 43, 91)( 44, 92)( 45, 93)( 46, 94)( 47, 95)( 48, 96)( 49, 97)( 50, 98)( 99,147)(100,148)(101,149)(102,150)(103,151)(104,152)(105,153)(106,154)(107,155)(108,156)(109,157)(110,158)(111,162)(112,163)(113,164)(114,159)(115,160)(116,161)(117,168)(118,169)(119,170)(120,165)(121,166)(122,167)(123,174)(124,175)(125,176)(126,171)(127,172)(128,173)(129,180)(130,181)(131,182)(132,177)(133,178)(134,179)(135,183)(136,184)(137,185)(138,186)(139,187)(140,188)(141,189)(142,190)(143,191)(144,192)(145,193)(146,194); poly := sub<Sym(194)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*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 >;