Overview
- Group
- SmallGroup(768,145174)
- Rank
- 4
- Schläfli Type
- {24,8,2}
- Vertices, edges, …
- 24, 96, 8, 2
- 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, 97)( 2, 99)( 3, 98)( 4,100)( 5,102)( 6,101)( 7,103)( 8,105)( 9,104)( 10,106)( 11,108)( 12,107)( 13,112)( 14,114)( 15,113)( 16,109)( 17,111)( 18,110)( 19,118)( 20,120)( 21,119)( 22,115)( 23,117)( 24,116)( 25,127)( 26,129)( 27,128)( 28,130)( 29,132)( 30,131)( 31,121)( 32,123)( 33,122)( 34,124)( 35,126)( 36,125)( 37,142)( 38,144)( 39,143)( 40,139)( 41,141)( 42,140)( 43,136)( 44,138)( 45,137)( 46,133)( 47,135)( 48,134)( 49,145)( 50,147)( 51,146)( 52,148)( 53,150)( 54,149)( 55,151)( 56,153)( 57,152)( 58,154)( 59,156)( 60,155)( 61,160)( 62,162)( 63,161)( 64,157)( 65,159)( 66,158)( 67,166)( 68,168)( 69,167)( 70,163)( 71,165)( 72,164)( 73,175)( 74,177)( 75,176)( 76,178)( 77,180)( 78,179)( 79,169)( 80,171)( 81,170)( 82,172)( 83,174)( 84,173)( 85,190)( 86,192)( 87,191)( 88,187)( 89,189)( 90,188)( 91,184)( 92,186)( 93,185)( 94,181)( 95,183)( 96,182);; s1 := ( 1, 2)( 4, 5)( 7, 8)( 10, 11)( 13, 17)( 14, 16)( 15, 18)( 19, 23)( 20, 22)( 21, 24)( 25, 32)( 26, 31)( 27, 33)( 28, 35)( 29, 34)( 30, 36)( 37, 47)( 38, 46)( 39, 48)( 40, 44)( 41, 43)( 42, 45)( 49, 62)( 50, 61)( 51, 63)( 52, 65)( 53, 64)( 54, 66)( 55, 68)( 56, 67)( 57, 69)( 58, 71)( 59, 70)( 60, 72)( 73, 92)( 74, 91)( 75, 93)( 76, 95)( 77, 94)( 78, 96)( 79, 86)( 80, 85)( 81, 87)( 82, 89)( 83, 88)( 84, 90)( 97,122)( 98,121)( 99,123)(100,125)(101,124)(102,126)(103,128)(104,127)(105,129)(106,131)(107,130)(108,132)(109,137)(110,136)(111,138)(112,134)(113,133)(114,135)(115,143)(116,142)(117,144)(118,140)(119,139)(120,141)(145,185)(146,184)(147,186)(148,182)(149,181)(150,183)(151,191)(152,190)(153,192)(154,188)(155,187)(156,189)(157,173)(158,172)(159,174)(160,170)(161,169)(162,171)(163,179)(164,178)(165,180)(166,176)(167,175)(168,177);; s2 := ( 1, 49)( 2, 50)( 3, 51)( 4, 52)( 5, 53)( 6, 54)( 7, 55)( 8, 56)( 9, 57)( 10, 58)( 11, 59)( 12, 60)( 13, 64)( 14, 65)( 15, 66)( 16, 61)( 17, 62)( 18, 63)( 19, 70)( 20, 71)( 21, 72)( 22, 67)( 23, 68)( 24, 69)( 25, 76)( 26, 77)( 27, 78)( 28, 73)( 29, 74)( 30, 75)( 31, 82)( 32, 83)( 33, 84)( 34, 79)( 35, 80)( 36, 81)( 37, 85)( 38, 86)( 39, 87)( 40, 88)( 41, 89)( 42, 90)( 43, 91)( 44, 92)( 45, 93)( 46, 94)( 47, 95)( 48, 96)( 97,145)( 98,146)( 99,147)(100,148)(101,149)(102,150)(103,151)(104,152)(105,153)(106,154)(107,155)(108,156)(109,160)(110,161)(111,162)(112,157)(113,158)(114,159)(115,166)(116,167)(117,168)(118,163)(119,164)(120,165)(121,172)(122,173)(123,174)(124,169)(125,170)(126,171)(127,178)(128,179)(129,180)(130,175)(131,176)(132,177)(133,181)(134,182)(135,183)(136,184)(137,185)(138,186)(139,187)(140,188)(141,189)(142,190)(143,191)(144,192);; s3 := (193,194);; 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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*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*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(194)!( 1, 97)( 2, 99)( 3, 98)( 4,100)( 5,102)( 6,101)( 7,103)( 8,105)( 9,104)( 10,106)( 11,108)( 12,107)( 13,112)( 14,114)( 15,113)( 16,109)( 17,111)( 18,110)( 19,118)( 20,120)( 21,119)( 22,115)( 23,117)( 24,116)( 25,127)( 26,129)( 27,128)( 28,130)( 29,132)( 30,131)( 31,121)( 32,123)( 33,122)( 34,124)( 35,126)( 36,125)( 37,142)( 38,144)( 39,143)( 40,139)( 41,141)( 42,140)( 43,136)( 44,138)( 45,137)( 46,133)( 47,135)( 48,134)( 49,145)( 50,147)( 51,146)( 52,148)( 53,150)( 54,149)( 55,151)( 56,153)( 57,152)( 58,154)( 59,156)( 60,155)( 61,160)( 62,162)( 63,161)( 64,157)( 65,159)( 66,158)( 67,166)( 68,168)( 69,167)( 70,163)( 71,165)( 72,164)( 73,175)( 74,177)( 75,176)( 76,178)( 77,180)( 78,179)( 79,169)( 80,171)( 81,170)( 82,172)( 83,174)( 84,173)( 85,190)( 86,192)( 87,191)( 88,187)( 89,189)( 90,188)( 91,184)( 92,186)( 93,185)( 94,181)( 95,183)( 96,182); s1 := Sym(194)!( 1, 2)( 4, 5)( 7, 8)( 10, 11)( 13, 17)( 14, 16)( 15, 18)( 19, 23)( 20, 22)( 21, 24)( 25, 32)( 26, 31)( 27, 33)( 28, 35)( 29, 34)( 30, 36)( 37, 47)( 38, 46)( 39, 48)( 40, 44)( 41, 43)( 42, 45)( 49, 62)( 50, 61)( 51, 63)( 52, 65)( 53, 64)( 54, 66)( 55, 68)( 56, 67)( 57, 69)( 58, 71)( 59, 70)( 60, 72)( 73, 92)( 74, 91)( 75, 93)( 76, 95)( 77, 94)( 78, 96)( 79, 86)( 80, 85)( 81, 87)( 82, 89)( 83, 88)( 84, 90)( 97,122)( 98,121)( 99,123)(100,125)(101,124)(102,126)(103,128)(104,127)(105,129)(106,131)(107,130)(108,132)(109,137)(110,136)(111,138)(112,134)(113,133)(114,135)(115,143)(116,142)(117,144)(118,140)(119,139)(120,141)(145,185)(146,184)(147,186)(148,182)(149,181)(150,183)(151,191)(152,190)(153,192)(154,188)(155,187)(156,189)(157,173)(158,172)(159,174)(160,170)(161,169)(162,171)(163,179)(164,178)(165,180)(166,176)(167,175)(168,177); s2 := Sym(194)!( 1, 49)( 2, 50)( 3, 51)( 4, 52)( 5, 53)( 6, 54)( 7, 55)( 8, 56)( 9, 57)( 10, 58)( 11, 59)( 12, 60)( 13, 64)( 14, 65)( 15, 66)( 16, 61)( 17, 62)( 18, 63)( 19, 70)( 20, 71)( 21, 72)( 22, 67)( 23, 68)( 24, 69)( 25, 76)( 26, 77)( 27, 78)( 28, 73)( 29, 74)( 30, 75)( 31, 82)( 32, 83)( 33, 84)( 34, 79)( 35, 80)( 36, 81)( 37, 85)( 38, 86)( 39, 87)( 40, 88)( 41, 89)( 42, 90)( 43, 91)( 44, 92)( 45, 93)( 46, 94)( 47, 95)( 48, 96)( 97,145)( 98,146)( 99,147)(100,148)(101,149)(102,150)(103,151)(104,152)(105,153)(106,154)(107,155)(108,156)(109,160)(110,161)(111,162)(112,157)(113,158)(114,159)(115,166)(116,167)(117,168)(118,163)(119,164)(120,165)(121,172)(122,173)(123,174)(124,169)(125,170)(126,171)(127,178)(128,179)(129,180)(130,175)(131,176)(132,177)(133,181)(134,182)(135,183)(136,184)(137,185)(138,186)(139,187)(140,188)(141,189)(142,190)(143,191)(144,192); s3 := Sym(194)!(193,194); 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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;