Overview
- Group
- SmallGroup(864,4000)
- Rank
- 3
- Schläfli Type
- {12,6}
- Vertices, edges, …
- 72, 216, 36
- Order of s0s1s2
- 6
- 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
9-fold
12-fold
18-fold
36-fold
72-fold
108-fold
Covers minimal covers in bold
2-fold
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*(s1*s0)^2*s1*s2*s1*s0*(s1*s2)^2*s1> of order 2
18 facets
- 18 of {12}*24
36 vertex figures
- 36 of {6}*12
P/N, where N=<s1*s0*(s2*s1)^2*(s0*s1)^4*s2> of order 2
18 facets
- 18 of {12}*24
36 vertex figures
- 36 of {6}*12
P/N, where N=<s0*s2*(s1*s0)^5*s1*s2, (s0*s1)^4*s2*s1*s0*(s2*s1)^2> of order 4
12 facets
18 vertex figures
- 18 of {6}*12
P/N, where N=<(s0*s1)^4, s2*(s1*s0)^2*s1*s2*s1*s0*(s1*s2)^2> of order 6
10 facets
12 vertex figures
- 12 of {6}*12
Representations
Permutation Representation (GAP)
s0 := ( 1, 3)( 2, 4)( 5, 11)( 6, 12)( 7, 9)( 8, 10)( 13, 27)( 14, 28)( 15, 25)( 16, 26)( 17, 35)( 18, 36)( 19, 33)( 20, 34)( 21, 31)( 22, 32)( 23, 29)( 24, 30)( 37, 39)( 38, 40)( 41, 47)( 42, 48)( 43, 45)( 44, 46)( 49, 63)( 50, 64)( 51, 61)( 52, 62)( 53, 71)( 54, 72)( 55, 69)( 56, 70)( 57, 67)( 58, 68)( 59, 65)( 60, 66)( 73, 75)( 74, 76)( 77, 83)( 78, 84)( 79, 81)( 80, 82)( 85, 99)( 86,100)( 87, 97)( 88, 98)( 89,107)( 90,108)( 91,105)( 92,106)( 93,103)( 94,104)( 95,101)( 96,102)(109,111)(110,112)(113,119)(114,120)(115,117)(116,118)(121,135)(122,136)(123,133)(124,134)(125,143)(126,144)(127,141)(128,142)(129,139)(130,140)(131,137)(132,138)(145,147)(146,148)(149,155)(150,156)(151,153)(152,154)(157,171)(158,172)(159,169)(160,170)(161,179)(162,180)(163,177)(164,178)(165,175)(166,176)(167,173)(168,174)(181,183)(182,184)(185,191)(186,192)(187,189)(188,190)(193,207)(194,208)(195,205)(196,206)(197,215)(198,216)(199,213)(200,214)(201,211)(202,212)(203,209)(204,210);; s1 := ( 1, 13)( 2, 15)( 3, 14)( 4, 16)( 5, 17)( 6, 19)( 7, 18)( 8, 20)( 9, 21)( 10, 23)( 11, 22)( 12, 24)( 26, 27)( 30, 31)( 34, 35)( 37, 85)( 38, 87)( 39, 86)( 40, 88)( 41, 89)( 42, 91)( 43, 90)( 44, 92)( 45, 93)( 46, 95)( 47, 94)( 48, 96)( 49, 73)( 50, 75)( 51, 74)( 52, 76)( 53, 77)( 54, 79)( 55, 78)( 56, 80)( 57, 81)( 58, 83)( 59, 82)( 60, 84)( 61, 97)( 62, 99)( 63, 98)( 64,100)( 65,101)( 66,103)( 67,102)( 68,104)( 69,105)( 70,107)( 71,106)( 72,108)(109,121)(110,123)(111,122)(112,124)(113,125)(114,127)(115,126)(116,128)(117,129)(118,131)(119,130)(120,132)(134,135)(138,139)(142,143)(145,193)(146,195)(147,194)(148,196)(149,197)(150,199)(151,198)(152,200)(153,201)(154,203)(155,202)(156,204)(157,181)(158,183)(159,182)(160,184)(161,185)(162,187)(163,186)(164,188)(165,189)(166,191)(167,190)(168,192)(169,205)(170,207)(171,206)(172,208)(173,209)(174,211)(175,210)(176,212)(177,213)(178,215)(179,214)(180,216);; s2 := ( 1,181)( 2,184)( 3,183)( 4,182)( 5,189)( 6,192)( 7,191)( 8,190)( 9,185)( 10,188)( 11,187)( 12,186)( 13,201)( 14,204)( 15,203)( 16,202)( 17,197)( 18,200)( 19,199)( 20,198)( 21,193)( 22,196)( 23,195)( 24,194)( 25,209)( 26,212)( 27,211)( 28,210)( 29,205)( 30,208)( 31,207)( 32,206)( 33,213)( 34,216)( 35,215)( 36,214)( 37,145)( 38,148)( 39,147)( 40,146)( 41,153)( 42,156)( 43,155)( 44,154)( 45,149)( 46,152)( 47,151)( 48,150)( 49,165)( 50,168)( 51,167)( 52,166)( 53,161)( 54,164)( 55,163)( 56,162)( 57,157)( 58,160)( 59,159)( 60,158)( 61,173)( 62,176)( 63,175)( 64,174)( 65,169)( 66,172)( 67,171)( 68,170)( 69,177)( 70,180)( 71,179)( 72,178)( 73,109)( 74,112)( 75,111)( 76,110)( 77,117)( 78,120)( 79,119)( 80,118)( 81,113)( 82,116)( 83,115)( 84,114)( 85,129)( 86,132)( 87,131)( 88,130)( 89,125)( 90,128)( 91,127)( 92,126)( 93,121)( 94,124)( 95,123)( 96,122)( 97,137)( 98,140)( 99,139)(100,138)(101,133)(102,136)(103,135)(104,134)(105,141)(106,144)(107,143)(108,142);; 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*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(216)!( 1, 3)( 2, 4)( 5, 11)( 6, 12)( 7, 9)( 8, 10)( 13, 27)( 14, 28)( 15, 25)( 16, 26)( 17, 35)( 18, 36)( 19, 33)( 20, 34)( 21, 31)( 22, 32)( 23, 29)( 24, 30)( 37, 39)( 38, 40)( 41, 47)( 42, 48)( 43, 45)( 44, 46)( 49, 63)( 50, 64)( 51, 61)( 52, 62)( 53, 71)( 54, 72)( 55, 69)( 56, 70)( 57, 67)( 58, 68)( 59, 65)( 60, 66)( 73, 75)( 74, 76)( 77, 83)( 78, 84)( 79, 81)( 80, 82)( 85, 99)( 86,100)( 87, 97)( 88, 98)( 89,107)( 90,108)( 91,105)( 92,106)( 93,103)( 94,104)( 95,101)( 96,102)(109,111)(110,112)(113,119)(114,120)(115,117)(116,118)(121,135)(122,136)(123,133)(124,134)(125,143)(126,144)(127,141)(128,142)(129,139)(130,140)(131,137)(132,138)(145,147)(146,148)(149,155)(150,156)(151,153)(152,154)(157,171)(158,172)(159,169)(160,170)(161,179)(162,180)(163,177)(164,178)(165,175)(166,176)(167,173)(168,174)(181,183)(182,184)(185,191)(186,192)(187,189)(188,190)(193,207)(194,208)(195,205)(196,206)(197,215)(198,216)(199,213)(200,214)(201,211)(202,212)(203,209)(204,210); s1 := Sym(216)!( 1, 13)( 2, 15)( 3, 14)( 4, 16)( 5, 17)( 6, 19)( 7, 18)( 8, 20)( 9, 21)( 10, 23)( 11, 22)( 12, 24)( 26, 27)( 30, 31)( 34, 35)( 37, 85)( 38, 87)( 39, 86)( 40, 88)( 41, 89)( 42, 91)( 43, 90)( 44, 92)( 45, 93)( 46, 95)( 47, 94)( 48, 96)( 49, 73)( 50, 75)( 51, 74)( 52, 76)( 53, 77)( 54, 79)( 55, 78)( 56, 80)( 57, 81)( 58, 83)( 59, 82)( 60, 84)( 61, 97)( 62, 99)( 63, 98)( 64,100)( 65,101)( 66,103)( 67,102)( 68,104)( 69,105)( 70,107)( 71,106)( 72,108)(109,121)(110,123)(111,122)(112,124)(113,125)(114,127)(115,126)(116,128)(117,129)(118,131)(119,130)(120,132)(134,135)(138,139)(142,143)(145,193)(146,195)(147,194)(148,196)(149,197)(150,199)(151,198)(152,200)(153,201)(154,203)(155,202)(156,204)(157,181)(158,183)(159,182)(160,184)(161,185)(162,187)(163,186)(164,188)(165,189)(166,191)(167,190)(168,192)(169,205)(170,207)(171,206)(172,208)(173,209)(174,211)(175,210)(176,212)(177,213)(178,215)(179,214)(180,216); s2 := Sym(216)!( 1,181)( 2,184)( 3,183)( 4,182)( 5,189)( 6,192)( 7,191)( 8,190)( 9,185)( 10,188)( 11,187)( 12,186)( 13,201)( 14,204)( 15,203)( 16,202)( 17,197)( 18,200)( 19,199)( 20,198)( 21,193)( 22,196)( 23,195)( 24,194)( 25,209)( 26,212)( 27,211)( 28,210)( 29,205)( 30,208)( 31,207)( 32,206)( 33,213)( 34,216)( 35,215)( 36,214)( 37,145)( 38,148)( 39,147)( 40,146)( 41,153)( 42,156)( 43,155)( 44,154)( 45,149)( 46,152)( 47,151)( 48,150)( 49,165)( 50,168)( 51,167)( 52,166)( 53,161)( 54,164)( 55,163)( 56,162)( 57,157)( 58,160)( 59,159)( 60,158)( 61,173)( 62,176)( 63,175)( 64,174)( 65,169)( 66,172)( 67,171)( 68,170)( 69,177)( 70,180)( 71,179)( 72,178)( 73,109)( 74,112)( 75,111)( 76,110)( 77,117)( 78,120)( 79,119)( 80,118)( 81,113)( 82,116)( 83,115)( 84,114)( 85,129)( 86,132)( 87,131)( 88,130)( 89,125)( 90,128)( 91,127)( 92,126)( 93,121)( 94,124)( 95,123)( 96,122)( 97,137)( 98,140)( 99,139)(100,138)(101,133)(102,136)(103,135)(104,134)(105,141)(106,144)(107,143)(108,142); 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*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 >;
References
None.
to this polytope.