Polytope of Type {28,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {28,18}*1008a
Also Known As : {28,18|2}. if this polytope has another name.
Group : SmallGroup(1008,158)
Rank : 3
Schlafli Type : {28,18}
Number of vertices, edges, etc : 28, 252, 18
Order of s₀s₁s₂ : 252
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {14,18}*504
   3-fold quotients : {28,6}*336a
   6-fold quotients : {14,6}*168
   7-fold quotients : {4,18}*144a
   9-fold quotients : {28,2}*112
   14-fold quotients : {2,18}*72
   18-fold quotients : {14,2}*56
   21-fold quotients : {4,6}*48a
   28-fold quotients : {2,9}*36
   36-fold quotients : {7,2}*28
   42-fold quotients : {2,6}*24
   63-fold quotients : {4,2}*16
   84-fold quotients : {2,3}*12
   126-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  4, 19)(  5, 20)(  6, 21)(  7, 16)(  8, 17)(  9, 18)( 10, 13)( 11, 14)
( 12, 15)( 25, 40)( 26, 41)( 27, 42)( 28, 37)( 29, 38)( 30, 39)( 31, 34)
( 32, 35)( 33, 36)( 46, 61)( 47, 62)( 48, 63)( 49, 58)( 50, 59)( 51, 60)
( 52, 55)( 53, 56)( 54, 57)( 67, 82)( 68, 83)( 69, 84)( 70, 79)( 71, 80)
( 72, 81)( 73, 76)( 74, 77)( 75, 78)( 88,103)( 89,104)( 90,105)( 91,100)
( 92,101)( 93,102)( 94, 97)( 95, 98)( 96, 99)(109,124)(110,125)(111,126)
(112,121)(113,122)(114,123)(115,118)(116,119)(117,120)(127,190)(128,191)
(129,192)(130,208)(131,209)(132,210)(133,205)(134,206)(135,207)(136,202)
(137,203)(138,204)(139,199)(140,200)(141,201)(142,196)(143,197)(144,198)
(145,193)(146,194)(147,195)(148,211)(149,212)(150,213)(151,229)(152,230)
(153,231)(154,226)(155,227)(156,228)(157,223)(158,224)(159,225)(160,220)
(161,221)(162,222)(163,217)(164,218)(165,219)(166,214)(167,215)(168,216)
(169,232)(170,233)(171,234)(172,250)(173,251)(174,252)(175,247)(176,248)
(177,249)(178,244)(179,245)(180,246)(181,241)(182,242)(183,243)(184,238)
(185,239)(186,240)(187,235)(188,236)(189,237);;
s1 := (  1,130)(  2,132)(  3,131)(  4,127)(  5,129)(  6,128)(  7,145)(  8,147)
(  9,146)( 10,142)( 11,144)( 12,143)( 13,139)( 14,141)( 15,140)( 16,136)
( 17,138)( 18,137)( 19,133)( 20,135)( 21,134)( 22,174)( 23,173)( 24,172)
( 25,171)( 26,170)( 27,169)( 28,189)( 29,188)( 30,187)( 31,186)( 32,185)
( 33,184)( 34,183)( 35,182)( 36,181)( 37,180)( 38,179)( 39,178)( 40,177)
( 41,176)( 42,175)( 43,153)( 44,152)( 45,151)( 46,150)( 47,149)( 48,148)
( 49,168)( 50,167)( 51,166)( 52,165)( 53,164)( 54,163)( 55,162)( 56,161)
( 57,160)( 58,159)( 59,158)( 60,157)( 61,156)( 62,155)( 63,154)( 64,193)
( 65,195)( 66,194)( 67,190)( 68,192)( 69,191)( 70,208)( 71,210)( 72,209)
( 73,205)( 74,207)( 75,206)( 76,202)( 77,204)( 78,203)( 79,199)( 80,201)
( 81,200)( 82,196)( 83,198)( 84,197)( 85,237)( 86,236)( 87,235)( 88,234)
( 89,233)( 90,232)( 91,252)( 92,251)( 93,250)( 94,249)( 95,248)( 96,247)
( 97,246)( 98,245)( 99,244)(100,243)(101,242)(102,241)(103,240)(104,239)
(105,238)(106,216)(107,215)(108,214)(109,213)(110,212)(111,211)(112,231)
(113,230)(114,229)(115,228)(116,227)(117,226)(118,225)(119,224)(120,223)
(121,222)(122,221)(123,220)(124,219)(125,218)(126,217);;
s2 := (  1, 22)(  2, 24)(  3, 23)(  4, 25)(  5, 27)(  6, 26)(  7, 28)(  8, 30)
(  9, 29)( 10, 31)( 11, 33)( 12, 32)( 13, 34)( 14, 36)( 15, 35)( 16, 37)
( 17, 39)( 18, 38)( 19, 40)( 20, 42)( 21, 41)( 43, 45)( 46, 48)( 49, 51)
( 52, 54)( 55, 57)( 58, 60)( 61, 63)( 64, 85)( 65, 87)( 66, 86)( 67, 88)
( 68, 90)( 69, 89)( 70, 91)( 71, 93)( 72, 92)( 73, 94)( 74, 96)( 75, 95)
( 76, 97)( 77, 99)( 78, 98)( 79,100)( 80,102)( 81,101)( 82,103)( 83,105)
( 84,104)(106,108)(109,111)(112,114)(115,117)(118,120)(121,123)(124,126)
(127,148)(128,150)(129,149)(130,151)(131,153)(132,152)(133,154)(134,156)
(135,155)(136,157)(137,159)(138,158)(139,160)(140,162)(141,161)(142,163)
(143,165)(144,164)(145,166)(146,168)(147,167)(169,171)(172,174)(175,177)
(178,180)(181,183)(184,186)(187,189)(190,211)(191,213)(192,212)(193,214)
(194,216)(195,215)(196,217)(197,219)(198,218)(199,220)(200,222)(201,221)
(202,223)(203,225)(204,224)(205,226)(206,228)(207,227)(208,229)(209,231)
(210,230)(232,234)(235,237)(238,240)(241,243)(244,246)(247,249)(250,252);;
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*s2*s1*s0*s1*s2*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, 
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*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(252)!(  4, 19)(  5, 20)(  6, 21)(  7, 16)(  8, 17)(  9, 18)( 10, 13)
( 11, 14)( 12, 15)( 25, 40)( 26, 41)( 27, 42)( 28, 37)( 29, 38)( 30, 39)
( 31, 34)( 32, 35)( 33, 36)( 46, 61)( 47, 62)( 48, 63)( 49, 58)( 50, 59)
( 51, 60)( 52, 55)( 53, 56)( 54, 57)( 67, 82)( 68, 83)( 69, 84)( 70, 79)
( 71, 80)( 72, 81)( 73, 76)( 74, 77)( 75, 78)( 88,103)( 89,104)( 90,105)
( 91,100)( 92,101)( 93,102)( 94, 97)( 95, 98)( 96, 99)(109,124)(110,125)
(111,126)(112,121)(113,122)(114,123)(115,118)(116,119)(117,120)(127,190)
(128,191)(129,192)(130,208)(131,209)(132,210)(133,205)(134,206)(135,207)
(136,202)(137,203)(138,204)(139,199)(140,200)(141,201)(142,196)(143,197)
(144,198)(145,193)(146,194)(147,195)(148,211)(149,212)(150,213)(151,229)
(152,230)(153,231)(154,226)(155,227)(156,228)(157,223)(158,224)(159,225)
(160,220)(161,221)(162,222)(163,217)(164,218)(165,219)(166,214)(167,215)
(168,216)(169,232)(170,233)(171,234)(172,250)(173,251)(174,252)(175,247)
(176,248)(177,249)(178,244)(179,245)(180,246)(181,241)(182,242)(183,243)
(184,238)(185,239)(186,240)(187,235)(188,236)(189,237);
s1 := Sym(252)!(  1,130)(  2,132)(  3,131)(  4,127)(  5,129)(  6,128)(  7,145)
(  8,147)(  9,146)( 10,142)( 11,144)( 12,143)( 13,139)( 14,141)( 15,140)
( 16,136)( 17,138)( 18,137)( 19,133)( 20,135)( 21,134)( 22,174)( 23,173)
( 24,172)( 25,171)( 26,170)( 27,169)( 28,189)( 29,188)( 30,187)( 31,186)
( 32,185)( 33,184)( 34,183)( 35,182)( 36,181)( 37,180)( 38,179)( 39,178)
( 40,177)( 41,176)( 42,175)( 43,153)( 44,152)( 45,151)( 46,150)( 47,149)
( 48,148)( 49,168)( 50,167)( 51,166)( 52,165)( 53,164)( 54,163)( 55,162)
( 56,161)( 57,160)( 58,159)( 59,158)( 60,157)( 61,156)( 62,155)( 63,154)
( 64,193)( 65,195)( 66,194)( 67,190)( 68,192)( 69,191)( 70,208)( 71,210)
( 72,209)( 73,205)( 74,207)( 75,206)( 76,202)( 77,204)( 78,203)( 79,199)
( 80,201)( 81,200)( 82,196)( 83,198)( 84,197)( 85,237)( 86,236)( 87,235)
( 88,234)( 89,233)( 90,232)( 91,252)( 92,251)( 93,250)( 94,249)( 95,248)
( 96,247)( 97,246)( 98,245)( 99,244)(100,243)(101,242)(102,241)(103,240)
(104,239)(105,238)(106,216)(107,215)(108,214)(109,213)(110,212)(111,211)
(112,231)(113,230)(114,229)(115,228)(116,227)(117,226)(118,225)(119,224)
(120,223)(121,222)(122,221)(123,220)(124,219)(125,218)(126,217);
s2 := Sym(252)!(  1, 22)(  2, 24)(  3, 23)(  4, 25)(  5, 27)(  6, 26)(  7, 28)
(  8, 30)(  9, 29)( 10, 31)( 11, 33)( 12, 32)( 13, 34)( 14, 36)( 15, 35)
( 16, 37)( 17, 39)( 18, 38)( 19, 40)( 20, 42)( 21, 41)( 43, 45)( 46, 48)
( 49, 51)( 52, 54)( 55, 57)( 58, 60)( 61, 63)( 64, 85)( 65, 87)( 66, 86)
( 67, 88)( 68, 90)( 69, 89)( 70, 91)( 71, 93)( 72, 92)( 73, 94)( 74, 96)
( 75, 95)( 76, 97)( 77, 99)( 78, 98)( 79,100)( 80,102)( 81,101)( 82,103)
( 83,105)( 84,104)(106,108)(109,111)(112,114)(115,117)(118,120)(121,123)
(124,126)(127,148)(128,150)(129,149)(130,151)(131,153)(132,152)(133,154)
(134,156)(135,155)(136,157)(137,159)(138,158)(139,160)(140,162)(141,161)
(142,163)(143,165)(144,164)(145,166)(146,168)(147,167)(169,171)(172,174)
(175,177)(178,180)(181,183)(184,186)(187,189)(190,211)(191,213)(192,212)
(193,214)(194,216)(195,215)(196,217)(197,219)(198,218)(199,220)(200,222)
(201,221)(202,223)(203,225)(204,224)(205,226)(206,228)(207,227)(208,229)
(209,231)(210,230)(232,234)(235,237)(238,240)(241,243)(244,246)(247,249)
(250,252);
poly := sub<Sym(252)|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*s2*s1*s0*s1*s2*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, 
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*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope