Overview
- Group
- SmallGroup(1728,12713)
- Rank
- 3
- Schläfli Type
- {4,24}
- Vertices, edges, …
- 36, 432, 216
- Order of s0s1s2
- 24
- Order of s0s1s2s1
- 12
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
8-fold
12-fold
24-fold
27-fold
54-fold
108-fold
216-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*s0*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 3
72 facets
- 72 of {4}*8
16 vertex figures
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4, 22)( 5, 24)( 6, 23)( 7, 18)( 8, 17)( 9, 16)( 10, 19)( 11, 21)( 12, 20)( 14, 15)( 25, 27)( 29, 30)( 31, 49)( 32, 51)( 33, 50)( 34, 45)( 35, 44)( 36, 43)( 37, 46)( 38, 48)( 39, 47)( 41, 42)( 52, 54)( 55, 82)( 56, 84)( 57, 83)( 58,103)( 59,105)( 60,104)( 61, 99)( 62, 98)( 63, 97)( 64,100)( 65,102)( 66,101)( 67, 94)( 68, 96)( 69, 95)( 70, 90)( 71, 89)( 72, 88)( 73, 91)( 74, 93)( 75, 92)( 76, 85)( 77, 87)( 78, 86)( 79,108)( 80,107)( 81,106)(110,111)(112,130)(113,132)(114,131)(115,126)(116,125)(117,124)(118,127)(119,129)(120,128)(122,123)(133,135)(137,138)(139,157)(140,159)(141,158)(142,153)(143,152)(144,151)(145,154)(146,156)(147,155)(149,150)(160,162)(163,190)(164,192)(165,191)(166,211)(167,213)(168,212)(169,207)(170,206)(171,205)(172,208)(173,210)(174,209)(175,202)(176,204)(177,203)(178,198)(179,197)(180,196)(181,199)(182,201)(183,200)(184,193)(185,195)(186,194)(187,216)(188,215)(189,214);; s1 := ( 2, 3)( 4, 5)( 7, 9)( 10, 25)( 11, 27)( 12, 26)( 13, 20)( 14, 19)( 15, 21)( 16, 24)( 17, 23)( 18, 22)( 29, 30)( 31, 32)( 34, 36)( 37, 52)( 38, 54)( 39, 53)( 40, 47)( 41, 46)( 42, 48)( 43, 51)( 44, 50)( 45, 49)( 55, 82)( 56, 84)( 57, 83)( 58, 86)( 59, 85)( 60, 87)( 61, 90)( 62, 89)( 63, 88)( 64,106)( 65,108)( 66,107)( 67,101)( 68,100)( 69,102)( 70,105)( 71,104)( 72,103)( 73, 95)( 74, 94)( 75, 96)( 76, 99)( 77, 98)( 78, 97)( 79, 91)( 80, 93)( 81, 92)(109,163)(110,165)(111,164)(112,167)(113,166)(114,168)(115,171)(116,170)(117,169)(118,187)(119,189)(120,188)(121,182)(122,181)(123,183)(124,186)(125,185)(126,184)(127,176)(128,175)(129,177)(130,180)(131,179)(132,178)(133,172)(134,174)(135,173)(136,190)(137,192)(138,191)(139,194)(140,193)(141,195)(142,198)(143,197)(144,196)(145,214)(146,216)(147,215)(148,209)(149,208)(150,210)(151,213)(152,212)(153,211)(154,203)(155,202)(156,204)(157,207)(158,206)(159,205)(160,199)(161,201)(162,200);; s2 := ( 1,148)( 2,149)( 3,150)( 4,146)( 5,147)( 6,145)( 7,153)( 8,151)( 9,152)( 10,141)( 11,139)( 12,140)( 13,136)( 14,137)( 15,138)( 16,143)( 17,144)( 18,142)( 19,158)( 20,159)( 21,157)( 22,156)( 23,154)( 24,155)( 25,160)( 26,161)( 27,162)( 28,121)( 29,122)( 30,123)( 31,119)( 32,120)( 33,118)( 34,126)( 35,124)( 36,125)( 37,114)( 38,112)( 39,113)( 40,109)( 41,110)( 42,111)( 43,116)( 44,117)( 45,115)( 46,131)( 47,132)( 48,130)( 49,129)( 50,127)( 51,128)( 52,133)( 53,134)( 54,135)( 55,175)( 56,176)( 57,177)( 58,173)( 59,174)( 60,172)( 61,180)( 62,178)( 63,179)( 64,168)( 65,166)( 66,167)( 67,163)( 68,164)( 69,165)( 70,170)( 71,171)( 72,169)( 73,185)( 74,186)( 75,184)( 76,183)( 77,181)( 78,182)( 79,187)( 80,188)( 81,189)( 82,202)( 83,203)( 84,204)( 85,200)( 86,201)( 87,199)( 88,207)( 89,205)( 90,206)( 91,195)( 92,193)( 93,194)( 94,190)( 95,191)( 96,192)( 97,197)( 98,198)( 99,196)(100,212)(101,213)(102,211)(103,210)(104,208)(105,209)(106,214)(107,215)(108,216);; 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,
s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(216)!( 2, 3)( 4, 22)( 5, 24)( 6, 23)( 7, 18)( 8, 17)( 9, 16)( 10, 19)( 11, 21)( 12, 20)( 14, 15)( 25, 27)( 29, 30)( 31, 49)( 32, 51)( 33, 50)( 34, 45)( 35, 44)( 36, 43)( 37, 46)( 38, 48)( 39, 47)( 41, 42)( 52, 54)( 55, 82)( 56, 84)( 57, 83)( 58,103)( 59,105)( 60,104)( 61, 99)( 62, 98)( 63, 97)( 64,100)( 65,102)( 66,101)( 67, 94)( 68, 96)( 69, 95)( 70, 90)( 71, 89)( 72, 88)( 73, 91)( 74, 93)( 75, 92)( 76, 85)( 77, 87)( 78, 86)( 79,108)( 80,107)( 81,106)(110,111)(112,130)(113,132)(114,131)(115,126)(116,125)(117,124)(118,127)(119,129)(120,128)(122,123)(133,135)(137,138)(139,157)(140,159)(141,158)(142,153)(143,152)(144,151)(145,154)(146,156)(147,155)(149,150)(160,162)(163,190)(164,192)(165,191)(166,211)(167,213)(168,212)(169,207)(170,206)(171,205)(172,208)(173,210)(174,209)(175,202)(176,204)(177,203)(178,198)(179,197)(180,196)(181,199)(182,201)(183,200)(184,193)(185,195)(186,194)(187,216)(188,215)(189,214); s1 := Sym(216)!( 2, 3)( 4, 5)( 7, 9)( 10, 25)( 11, 27)( 12, 26)( 13, 20)( 14, 19)( 15, 21)( 16, 24)( 17, 23)( 18, 22)( 29, 30)( 31, 32)( 34, 36)( 37, 52)( 38, 54)( 39, 53)( 40, 47)( 41, 46)( 42, 48)( 43, 51)( 44, 50)( 45, 49)( 55, 82)( 56, 84)( 57, 83)( 58, 86)( 59, 85)( 60, 87)( 61, 90)( 62, 89)( 63, 88)( 64,106)( 65,108)( 66,107)( 67,101)( 68,100)( 69,102)( 70,105)( 71,104)( 72,103)( 73, 95)( 74, 94)( 75, 96)( 76, 99)( 77, 98)( 78, 97)( 79, 91)( 80, 93)( 81, 92)(109,163)(110,165)(111,164)(112,167)(113,166)(114,168)(115,171)(116,170)(117,169)(118,187)(119,189)(120,188)(121,182)(122,181)(123,183)(124,186)(125,185)(126,184)(127,176)(128,175)(129,177)(130,180)(131,179)(132,178)(133,172)(134,174)(135,173)(136,190)(137,192)(138,191)(139,194)(140,193)(141,195)(142,198)(143,197)(144,196)(145,214)(146,216)(147,215)(148,209)(149,208)(150,210)(151,213)(152,212)(153,211)(154,203)(155,202)(156,204)(157,207)(158,206)(159,205)(160,199)(161,201)(162,200); s2 := Sym(216)!( 1,148)( 2,149)( 3,150)( 4,146)( 5,147)( 6,145)( 7,153)( 8,151)( 9,152)( 10,141)( 11,139)( 12,140)( 13,136)( 14,137)( 15,138)( 16,143)( 17,144)( 18,142)( 19,158)( 20,159)( 21,157)( 22,156)( 23,154)( 24,155)( 25,160)( 26,161)( 27,162)( 28,121)( 29,122)( 30,123)( 31,119)( 32,120)( 33,118)( 34,126)( 35,124)( 36,125)( 37,114)( 38,112)( 39,113)( 40,109)( 41,110)( 42,111)( 43,116)( 44,117)( 45,115)( 46,131)( 47,132)( 48,130)( 49,129)( 50,127)( 51,128)( 52,133)( 53,134)( 54,135)( 55,175)( 56,176)( 57,177)( 58,173)( 59,174)( 60,172)( 61,180)( 62,178)( 63,179)( 64,168)( 65,166)( 66,167)( 67,163)( 68,164)( 69,165)( 70,170)( 71,171)( 72,169)( 73,185)( 74,186)( 75,184)( 76,183)( 77,181)( 78,182)( 79,187)( 80,188)( 81,189)( 82,202)( 83,203)( 84,204)( 85,200)( 86,201)( 87,199)( 88,207)( 89,205)( 90,206)( 91,195)( 92,193)( 93,194)( 94,190)( 95,191)( 96,192)( 97,197)( 98,198)( 99,196)(100,212)(101,213)(102,211)(103,210)(104,208)(105,209)(106,214)(107,215)(108,216); poly := sub<Sym(216)|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, s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0 >;
References
None.
to this polytope.