Overview
- Group
- SmallGroup(1792,90280)
- Rank
- 3
- Schläfli Type
- {4,28}
- Vertices, edges, …
- 32, 448, 224
- Order of s0s1s2
- 56
- Order of s0s1s2s1
- 8
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
2-fold
4-fold
7-fold
8-fold
14-fold
16-fold
28-fold
32-fold
56-fold
64-fold
112-fold
224-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=<s0*s1*(s2*s1*s0)^2*s1*s2*s1*s0*s2*s1> of order 2
112 facets
- 112 of {4}*8
16 vertex figures
- 16 of {28}*56
P/N, where N=<s0*(s2*s1*s0*s1)^3*s2*s1> of order 2
112 facets
- 112 of {4}*8
16 vertex figures
- 16 of {28}*56
P/N, where N=<(s0*s1)^2, (s0*s2*s1)^2*s0*s1*s2*s1*s0*s2> of order 4
70 facets
8 vertex figures
- 8 of {28}*56
P/N, where N=<s0*s1*(s2*s1*s0)^2*s1*s2*s1*s0*s2*s1, s0*s1*s0*s2*s1*s0*(s2*s1)^2*s0*(s2*s1)^10*s2> of order 4
56 facets
- 56 of {4}*8
8 vertex figures
- 8 of {28}*56
P/N, where N=<s0*s1*(s2*s1*s0)^2*s1*s2*s1*s0*s2*s1, (s1*s2)^14> of order 4
56 facets
- 56 of {4}*8
10 vertex figures
P/N, where N=<(s0*s1)^2, (s0*s1*s2*s1)^3*s0*s1*s2> of order 4
63 facets
8 vertex figures
- 8 of {28}*56
P/N, where N=<s0*(s2*s1*s0*s1)^3*s2*s1, s1*s0*(s2*s1)^2*s0*(s2*s1)^11*s2> of order 4
56 facets
- 56 of {4}*8
9 vertex figures
Representations
Permutation Representation (GAP)
s0 := ( 15, 22)( 16, 23)( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 43, 50)( 44, 51)( 45, 52)( 46, 53)( 47, 54)( 48, 55)( 49, 56)( 57,106)( 58,107)( 59,108)( 60,109)( 61,110)( 62,111)( 63,112)( 64, 99)( 65,100)( 66,101)( 67,102)( 68,103)( 69,104)( 70,105)( 71, 85)( 72, 86)( 73, 87)( 74, 88)( 75, 89)( 76, 90)( 77, 91)( 78, 92)( 79, 93)( 80, 94)( 81, 95)( 82, 96)( 83, 97)( 84, 98)(127,134)(128,135)(129,136)(130,137)(131,138)(132,139)(133,140)(155,162)(156,163)(157,164)(158,165)(159,166)(160,167)(161,168)(169,218)(170,219)(171,220)(172,221)(173,222)(174,223)(175,224)(176,211)(177,212)(178,213)(179,214)(180,215)(181,216)(182,217)(183,197)(184,198)(185,199)(186,200)(187,201)(188,202)(189,203)(190,204)(191,205)(192,206)(193,207)(194,208)(195,209)(196,210);; s1 := ( 2, 7)( 3, 6)( 4, 5)( 9, 14)( 10, 13)( 11, 12)( 16, 21)( 17, 20)( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 29, 43)( 30, 49)( 31, 48)( 32, 47)( 33, 46)( 34, 45)( 35, 44)( 36, 50)( 37, 56)( 38, 55)( 39, 54)( 40, 53)( 41, 52)( 42, 51)( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)( 67, 68)( 72, 77)( 73, 76)( 74, 75)( 79, 84)( 80, 83)( 81, 82)( 85, 99)( 86,105)( 87,104)( 88,103)( 89,102)( 90,101)( 91,100)( 92,106)( 93,112)( 94,111)( 95,110)( 96,109)( 97,108)( 98,107)(113,169)(114,175)(115,174)(116,173)(117,172)(118,171)(119,170)(120,176)(121,182)(122,181)(123,180)(124,179)(125,178)(126,177)(127,183)(128,189)(129,188)(130,187)(131,186)(132,185)(133,184)(134,190)(135,196)(136,195)(137,194)(138,193)(139,192)(140,191)(141,211)(142,217)(143,216)(144,215)(145,214)(146,213)(147,212)(148,218)(149,224)(150,223)(151,222)(152,221)(153,220)(154,219)(155,197)(156,203)(157,202)(158,201)(159,200)(160,199)(161,198)(162,204)(163,210)(164,209)(165,208)(166,207)(167,206)(168,205);; s2 := ( 1,114)( 2,113)( 3,119)( 4,118)( 5,117)( 6,116)( 7,115)( 8,121)( 9,120)( 10,126)( 11,125)( 12,124)( 13,123)( 14,122)( 15,135)( 16,134)( 17,140)( 18,139)( 19,138)( 20,137)( 21,136)( 22,128)( 23,127)( 24,133)( 25,132)( 26,131)( 27,130)( 28,129)( 29,149)( 30,148)( 31,154)( 32,153)( 33,152)( 34,151)( 35,150)( 36,142)( 37,141)( 38,147)( 39,146)( 40,145)( 41,144)( 42,143)( 43,156)( 44,155)( 45,161)( 46,160)( 47,159)( 48,158)( 49,157)( 50,163)( 51,162)( 52,168)( 53,167)( 54,166)( 55,165)( 56,164)( 57,170)( 58,169)( 59,175)( 60,174)( 61,173)( 62,172)( 63,171)( 64,177)( 65,176)( 66,182)( 67,181)( 68,180)( 69,179)( 70,178)( 71,191)( 72,190)( 73,196)( 74,195)( 75,194)( 76,193)( 77,192)( 78,184)( 79,183)( 80,189)( 81,188)( 82,187)( 83,186)( 84,185)( 85,205)( 86,204)( 87,210)( 88,209)( 89,208)( 90,207)( 91,206)( 92,198)( 93,197)( 94,203)( 95,202)( 96,201)( 97,200)( 98,199)( 99,212)(100,211)(101,217)(102,216)(103,215)(104,214)(105,213)(106,219)(107,218)(108,224)(109,223)(110,222)(111,221)(112,220);; 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*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s0*s1*s2*s0*s1*s2*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*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(224)!( 15, 22)( 16, 23)( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 43, 50)( 44, 51)( 45, 52)( 46, 53)( 47, 54)( 48, 55)( 49, 56)( 57,106)( 58,107)( 59,108)( 60,109)( 61,110)( 62,111)( 63,112)( 64, 99)( 65,100)( 66,101)( 67,102)( 68,103)( 69,104)( 70,105)( 71, 85)( 72, 86)( 73, 87)( 74, 88)( 75, 89)( 76, 90)( 77, 91)( 78, 92)( 79, 93)( 80, 94)( 81, 95)( 82, 96)( 83, 97)( 84, 98)(127,134)(128,135)(129,136)(130,137)(131,138)(132,139)(133,140)(155,162)(156,163)(157,164)(158,165)(159,166)(160,167)(161,168)(169,218)(170,219)(171,220)(172,221)(173,222)(174,223)(175,224)(176,211)(177,212)(178,213)(179,214)(180,215)(181,216)(182,217)(183,197)(184,198)(185,199)(186,200)(187,201)(188,202)(189,203)(190,204)(191,205)(192,206)(193,207)(194,208)(195,209)(196,210); s1 := Sym(224)!( 2, 7)( 3, 6)( 4, 5)( 9, 14)( 10, 13)( 11, 12)( 16, 21)( 17, 20)( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 29, 43)( 30, 49)( 31, 48)( 32, 47)( 33, 46)( 34, 45)( 35, 44)( 36, 50)( 37, 56)( 38, 55)( 39, 54)( 40, 53)( 41, 52)( 42, 51)( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)( 67, 68)( 72, 77)( 73, 76)( 74, 75)( 79, 84)( 80, 83)( 81, 82)( 85, 99)( 86,105)( 87,104)( 88,103)( 89,102)( 90,101)( 91,100)( 92,106)( 93,112)( 94,111)( 95,110)( 96,109)( 97,108)( 98,107)(113,169)(114,175)(115,174)(116,173)(117,172)(118,171)(119,170)(120,176)(121,182)(122,181)(123,180)(124,179)(125,178)(126,177)(127,183)(128,189)(129,188)(130,187)(131,186)(132,185)(133,184)(134,190)(135,196)(136,195)(137,194)(138,193)(139,192)(140,191)(141,211)(142,217)(143,216)(144,215)(145,214)(146,213)(147,212)(148,218)(149,224)(150,223)(151,222)(152,221)(153,220)(154,219)(155,197)(156,203)(157,202)(158,201)(159,200)(160,199)(161,198)(162,204)(163,210)(164,209)(165,208)(166,207)(167,206)(168,205); s2 := Sym(224)!( 1,114)( 2,113)( 3,119)( 4,118)( 5,117)( 6,116)( 7,115)( 8,121)( 9,120)( 10,126)( 11,125)( 12,124)( 13,123)( 14,122)( 15,135)( 16,134)( 17,140)( 18,139)( 19,138)( 20,137)( 21,136)( 22,128)( 23,127)( 24,133)( 25,132)( 26,131)( 27,130)( 28,129)( 29,149)( 30,148)( 31,154)( 32,153)( 33,152)( 34,151)( 35,150)( 36,142)( 37,141)( 38,147)( 39,146)( 40,145)( 41,144)( 42,143)( 43,156)( 44,155)( 45,161)( 46,160)( 47,159)( 48,158)( 49,157)( 50,163)( 51,162)( 52,168)( 53,167)( 54,166)( 55,165)( 56,164)( 57,170)( 58,169)( 59,175)( 60,174)( 61,173)( 62,172)( 63,171)( 64,177)( 65,176)( 66,182)( 67,181)( 68,180)( 69,179)( 70,178)( 71,191)( 72,190)( 73,196)( 74,195)( 75,194)( 76,193)( 77,192)( 78,184)( 79,183)( 80,189)( 81,188)( 82,187)( 83,186)( 84,185)( 85,205)( 86,204)( 87,210)( 88,209)( 89,208)( 90,207)( 91,206)( 92,198)( 93,197)( 94,203)( 95,202)( 96,201)( 97,200)( 98,199)( 99,212)(100,211)(101,217)(102,216)(103,215)(104,214)(105,213)(106,219)(107,218)(108,224)(109,223)(110,222)(111,221)(112,220); poly := sub<Sym(224)|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*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s0*s1*s2*s0*s1*s2*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*s1*s2*s1*s2 >;
References
None.
to this polytope.