Overview
- Group
- SmallGroup(768,1090183)
- Rank
- 4
- Schläfli Type
- {4,6,4}
- Vertices, edges, …
- 4, 48, 48, 16
- Order of s0s1s2s3
- 12
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
16-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.
P/N, where N=<(s1*s2*s3*s2)^2> of order 2
8 facets
- 8 of {4,6}*48c
4 vertex figures
- 4 of 2-fold non-regular quotient of {6,4}*192b
P/N, where N=<s2*s1*s2*s3*s2*s1*s3*s2> of order 2
8 facets
- 8 of {4,6}*48c
4 vertex figures
- 4 of 2-fold non-regular quotient of {6,4}*192b
P/N, where N=<s1*s2*s3*s2*s1*(s2*s3)^2> of order 2
8 facets
- 8 of {4,6}*48c
4 vertex figures
- 4 of 2-fold non-regular quotient of {6,4}*192b
P/N, where N=<(s1*s2)^3> of order 2
12 facets
4 vertex figures
- 4 of 2-fold non-regular quotient of {6,4}*192b
P/N, where N=<(s2*s3)^2, s1*s2*s3*s2*s1*s3> of order 4
4 facets
- 4 of {4,6}*48c
4 vertex figures
- 4 of 4-fold non-regular quotient of {6,4}*192b
P/N, where N=<(s1*s2)^3, s1*(s2*s1*s3)^2*s2> of order 4
6 facets
4 vertex figures
- 4 of 4-fold non-regular quotient of {6,4}*192b
Representations
Permutation Representation (GAP)
s0 := ( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9, 12)( 10, 11)( 13, 16)( 14, 15)( 17, 20)( 18, 19)( 21, 24)( 22, 23)( 25, 28)( 26, 27)( 29, 32)( 30, 31)( 33, 36)( 34, 35)( 37, 40)( 38, 39)( 41, 44)( 42, 43)( 45, 48)( 46, 47)( 49, 52)( 50, 51)( 53, 56)( 54, 55)( 57, 60)( 58, 59)( 61, 64)( 62, 63)( 65, 68)( 66, 67)( 69, 72)( 70, 71)( 73, 76)( 74, 75)( 77, 80)( 78, 79)( 81, 84)( 82, 83)( 85, 88)( 86, 87)( 89, 92)( 90, 91)( 93, 96)( 94, 95)( 97,100)( 98, 99)(101,104)(102,103)(105,108)(106,107)(109,112)(110,111)(113,116)(114,115)(117,120)(118,119)(121,124)(122,123)(125,128)(126,127)(129,132)(130,131)(133,136)(134,135)(137,140)(138,139)(141,144)(142,143)(145,148)(146,147)(149,152)(150,151)(153,156)(154,155)(157,160)(158,159)(161,164)(162,163)(165,168)(166,167)(169,172)(170,171)(173,176)(174,175)(177,180)(178,179)(181,184)(182,183)(185,188)(186,187)(189,192)(190,191);; s1 := ( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)( 26, 46)( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 51, 52)( 55, 56)( 57, 61)( 58, 62)( 59, 64)( 60, 63)( 65, 81)( 66, 82)( 67, 84)( 68, 83)( 69, 85)( 70, 86)( 71, 88)( 72, 87)( 73, 93)( 74, 94)( 75, 96)( 76, 95)( 77, 89)( 78, 90)( 79, 92)( 80, 91)( 99,100)(103,104)(105,109)(106,110)(107,112)(108,111)(113,129)(114,130)(115,132)(116,131)(117,133)(118,134)(119,136)(120,135)(121,141)(122,142)(123,144)(124,143)(125,137)(126,138)(127,140)(128,139)(147,148)(151,152)(153,157)(154,158)(155,160)(156,159)(161,177)(162,178)(163,180)(164,179)(165,181)(166,182)(167,184)(168,183)(169,189)(170,190)(171,192)(172,191)(173,185)(174,186)(175,188)(176,187);; s2 := ( 1, 33)( 2, 35)( 3, 34)( 4, 36)( 5, 41)( 6, 43)( 7, 42)( 8, 44)( 9, 37)( 10, 39)( 11, 38)( 12, 40)( 13, 45)( 14, 47)( 15, 46)( 16, 48)( 18, 19)( 21, 25)( 22, 27)( 23, 26)( 24, 28)( 30, 31)( 49, 81)( 50, 83)( 51, 82)( 52, 84)( 53, 89)( 54, 91)( 55, 90)( 56, 92)( 57, 85)( 58, 87)( 59, 86)( 60, 88)( 61, 93)( 62, 95)( 63, 94)( 64, 96)( 66, 67)( 69, 73)( 70, 75)( 71, 74)( 72, 76)( 78, 79)( 97,177)( 98,179)( 99,178)(100,180)(101,185)(102,187)(103,186)(104,188)(105,181)(106,183)(107,182)(108,184)(109,189)(110,191)(111,190)(112,192)(113,161)(114,163)(115,162)(116,164)(117,169)(118,171)(119,170)(120,172)(121,165)(122,167)(123,166)(124,168)(125,173)(126,175)(127,174)(128,176)(129,145)(130,147)(131,146)(132,148)(133,153)(134,155)(135,154)(136,156)(137,149)(138,151)(139,150)(140,152)(141,157)(142,159)(143,158)(144,160);; s3 := ( 1,101)( 2,102)( 3,103)( 4,104)( 5, 97)( 6, 98)( 7, 99)( 8,100)( 9,109)( 10,110)( 11,111)( 12,112)( 13,105)( 14,106)( 15,107)( 16,108)( 17,117)( 18,118)( 19,119)( 20,120)( 21,113)( 22,114)( 23,115)( 24,116)( 25,125)( 26,126)( 27,127)( 28,128)( 29,121)( 30,122)( 31,123)( 32,124)( 33,133)( 34,134)( 35,135)( 36,136)( 37,129)( 38,130)( 39,131)( 40,132)( 41,141)( 42,142)( 43,143)( 44,144)( 45,137)( 46,138)( 47,139)( 48,140)( 49,149)( 50,150)( 51,151)( 52,152)( 53,145)( 54,146)( 55,147)( 56,148)( 57,157)( 58,158)( 59,159)( 60,160)( 61,153)( 62,154)( 63,155)( 64,156)( 65,165)( 66,166)( 67,167)( 68,168)( 69,161)( 70,162)( 71,163)( 72,164)( 73,173)( 74,174)( 75,175)( 76,176)( 77,169)( 78,170)( 79,171)( 80,172)( 81,181)( 82,182)( 83,183)( 84,184)( 85,177)( 86,178)( 87,179)( 88,180)( 89,189)( 90,190)( 91,191)( 92,192)( 93,185)( 94,186)( 95,187)( 96,188);; 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*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(192)!( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9, 12)( 10, 11)( 13, 16)( 14, 15)( 17, 20)( 18, 19)( 21, 24)( 22, 23)( 25, 28)( 26, 27)( 29, 32)( 30, 31)( 33, 36)( 34, 35)( 37, 40)( 38, 39)( 41, 44)( 42, 43)( 45, 48)( 46, 47)( 49, 52)( 50, 51)( 53, 56)( 54, 55)( 57, 60)( 58, 59)( 61, 64)( 62, 63)( 65, 68)( 66, 67)( 69, 72)( 70, 71)( 73, 76)( 74, 75)( 77, 80)( 78, 79)( 81, 84)( 82, 83)( 85, 88)( 86, 87)( 89, 92)( 90, 91)( 93, 96)( 94, 95)( 97,100)( 98, 99)(101,104)(102,103)(105,108)(106,107)(109,112)(110,111)(113,116)(114,115)(117,120)(118,119)(121,124)(122,123)(125,128)(126,127)(129,132)(130,131)(133,136)(134,135)(137,140)(138,139)(141,144)(142,143)(145,148)(146,147)(149,152)(150,151)(153,156)(154,155)(157,160)(158,159)(161,164)(162,163)(165,168)(166,167)(169,172)(170,171)(173,176)(174,175)(177,180)(178,179)(181,184)(182,183)(185,188)(186,187)(189,192)(190,191); s1 := Sym(192)!( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)( 26, 46)( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 51, 52)( 55, 56)( 57, 61)( 58, 62)( 59, 64)( 60, 63)( 65, 81)( 66, 82)( 67, 84)( 68, 83)( 69, 85)( 70, 86)( 71, 88)( 72, 87)( 73, 93)( 74, 94)( 75, 96)( 76, 95)( 77, 89)( 78, 90)( 79, 92)( 80, 91)( 99,100)(103,104)(105,109)(106,110)(107,112)(108,111)(113,129)(114,130)(115,132)(116,131)(117,133)(118,134)(119,136)(120,135)(121,141)(122,142)(123,144)(124,143)(125,137)(126,138)(127,140)(128,139)(147,148)(151,152)(153,157)(154,158)(155,160)(156,159)(161,177)(162,178)(163,180)(164,179)(165,181)(166,182)(167,184)(168,183)(169,189)(170,190)(171,192)(172,191)(173,185)(174,186)(175,188)(176,187); s2 := Sym(192)!( 1, 33)( 2, 35)( 3, 34)( 4, 36)( 5, 41)( 6, 43)( 7, 42)( 8, 44)( 9, 37)( 10, 39)( 11, 38)( 12, 40)( 13, 45)( 14, 47)( 15, 46)( 16, 48)( 18, 19)( 21, 25)( 22, 27)( 23, 26)( 24, 28)( 30, 31)( 49, 81)( 50, 83)( 51, 82)( 52, 84)( 53, 89)( 54, 91)( 55, 90)( 56, 92)( 57, 85)( 58, 87)( 59, 86)( 60, 88)( 61, 93)( 62, 95)( 63, 94)( 64, 96)( 66, 67)( 69, 73)( 70, 75)( 71, 74)( 72, 76)( 78, 79)( 97,177)( 98,179)( 99,178)(100,180)(101,185)(102,187)(103,186)(104,188)(105,181)(106,183)(107,182)(108,184)(109,189)(110,191)(111,190)(112,192)(113,161)(114,163)(115,162)(116,164)(117,169)(118,171)(119,170)(120,172)(121,165)(122,167)(123,166)(124,168)(125,173)(126,175)(127,174)(128,176)(129,145)(130,147)(131,146)(132,148)(133,153)(134,155)(135,154)(136,156)(137,149)(138,151)(139,150)(140,152)(141,157)(142,159)(143,158)(144,160); s3 := Sym(192)!( 1,101)( 2,102)( 3,103)( 4,104)( 5, 97)( 6, 98)( 7, 99)( 8,100)( 9,109)( 10,110)( 11,111)( 12,112)( 13,105)( 14,106)( 15,107)( 16,108)( 17,117)( 18,118)( 19,119)( 20,120)( 21,113)( 22,114)( 23,115)( 24,116)( 25,125)( 26,126)( 27,127)( 28,128)( 29,121)( 30,122)( 31,123)( 32,124)( 33,133)( 34,134)( 35,135)( 36,136)( 37,129)( 38,130)( 39,131)( 40,132)( 41,141)( 42,142)( 43,143)( 44,144)( 45,137)( 46,138)( 47,139)( 48,140)( 49,149)( 50,150)( 51,151)( 52,152)( 53,145)( 54,146)( 55,147)( 56,148)( 57,157)( 58,158)( 59,159)( 60,160)( 61,153)( 62,154)( 63,155)( 64,156)( 65,165)( 66,166)( 67,167)( 68,168)( 69,161)( 70,162)( 71,163)( 72,164)( 73,173)( 74,174)( 75,175)( 76,176)( 77,169)( 78,170)( 79,171)( 80,172)( 81,181)( 82,182)( 83,183)( 84,184)( 85,177)( 86,178)( 87,179)( 88,180)( 89,189)( 90,190)( 91,191)( 92,192)( 93,185)( 94,186)( 95,187)( 96,188); poly := sub<Sym(192)|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*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2 >;
References
None.
to this polytope.