Overview
- Group
- SmallGroup(552,25)
- Rank
- 2
- Schläfli Type
- {276}
- Vertices, edges, …
- 276, 276
- Order of s0s1
- 276
- Also known as
- 276-gon, {276}. if this polytope has another name.
Special Properties
- Universal
- Spherical
- Locally Spherical
- Orientable
- Self-Dual
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
12-fold
23-fold
46-fold
69-fold
92-fold
138-fold
Covers minimal covers in bold
2-fold
3-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 23)( 3, 22)( 4, 21)( 5, 20)( 6, 19)( 7, 18)( 8, 17)( 9, 16)( 10, 15)( 11, 14)( 12, 13)( 24, 47)( 25, 69)( 26, 68)( 27, 67)( 28, 66)( 29, 65)( 30, 64)( 31, 63)( 32, 62)( 33, 61)( 34, 60)( 35, 59)( 36, 58)( 37, 57)( 38, 56)( 39, 55)( 40, 54)( 41, 53)( 42, 52)( 43, 51)( 44, 50)( 45, 49)( 46, 48)( 71, 92)( 72, 91)( 73, 90)( 74, 89)( 75, 88)( 76, 87)( 77, 86)( 78, 85)( 79, 84)( 80, 83)( 81, 82)( 93,116)( 94,138)( 95,137)( 96,136)( 97,135)( 98,134)( 99,133)(100,132)(101,131)(102,130)(103,129)(104,128)(105,127)(106,126)(107,125)(108,124)(109,123)(110,122)(111,121)(112,120)(113,119)(114,118)(115,117)(139,208)(140,230)(141,229)(142,228)(143,227)(144,226)(145,225)(146,224)(147,223)(148,222)(149,221)(150,220)(151,219)(152,218)(153,217)(154,216)(155,215)(156,214)(157,213)(158,212)(159,211)(160,210)(161,209)(162,254)(163,276)(164,275)(165,274)(166,273)(167,272)(168,271)(169,270)(170,269)(171,268)(172,267)(173,266)(174,265)(175,264)(176,263)(177,262)(178,261)(179,260)(180,259)(181,258)(182,257)(183,256)(184,255)(185,231)(186,253)(187,252)(188,251)(189,250)(190,249)(191,248)(192,247)(193,246)(194,245)(195,244)(196,243)(197,242)(198,241)(199,240)(200,239)(201,238)(202,237)(203,236)(204,235)(205,234)(206,233)(207,232);; s1 := ( 1,163)( 2,162)( 3,184)( 4,183)( 5,182)( 6,181)( 7,180)( 8,179)( 9,178)( 10,177)( 11,176)( 12,175)( 13,174)( 14,173)( 15,172)( 16,171)( 17,170)( 18,169)( 19,168)( 20,167)( 21,166)( 22,165)( 23,164)( 24,140)( 25,139)( 26,161)( 27,160)( 28,159)( 29,158)( 30,157)( 31,156)( 32,155)( 33,154)( 34,153)( 35,152)( 36,151)( 37,150)( 38,149)( 39,148)( 40,147)( 41,146)( 42,145)( 43,144)( 44,143)( 45,142)( 46,141)( 47,186)( 48,185)( 49,207)( 50,206)( 51,205)( 52,204)( 53,203)( 54,202)( 55,201)( 56,200)( 57,199)( 58,198)( 59,197)( 60,196)( 61,195)( 62,194)( 63,193)( 64,192)( 65,191)( 66,190)( 67,189)( 68,188)( 69,187)( 70,232)( 71,231)( 72,253)( 73,252)( 74,251)( 75,250)( 76,249)( 77,248)( 78,247)( 79,246)( 80,245)( 81,244)( 82,243)( 83,242)( 84,241)( 85,240)( 86,239)( 87,238)( 88,237)( 89,236)( 90,235)( 91,234)( 92,233)( 93,209)( 94,208)( 95,230)( 96,229)( 97,228)( 98,227)( 99,226)(100,225)(101,224)(102,223)(103,222)(104,221)(105,220)(106,219)(107,218)(108,217)(109,216)(110,215)(111,214)(112,213)(113,212)(114,211)(115,210)(116,255)(117,254)(118,276)(119,275)(120,274)(121,273)(122,272)(123,271)(124,270)(125,269)(126,268)(127,267)(128,266)(129,265)(130,264)(131,263)(132,262)(133,261)(134,260)(135,259)(136,258)(137,257)(138,256);; poly := Group([s0,s1]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1");;
s0 := F.1;; s1 := F.2;;
rels := [ s0*s0, s1*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*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*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*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*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*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*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*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*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*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(276)!( 2, 23)( 3, 22)( 4, 21)( 5, 20)( 6, 19)( 7, 18)( 8, 17)( 9, 16)( 10, 15)( 11, 14)( 12, 13)( 24, 47)( 25, 69)( 26, 68)( 27, 67)( 28, 66)( 29, 65)( 30, 64)( 31, 63)( 32, 62)( 33, 61)( 34, 60)( 35, 59)( 36, 58)( 37, 57)( 38, 56)( 39, 55)( 40, 54)( 41, 53)( 42, 52)( 43, 51)( 44, 50)( 45, 49)( 46, 48)( 71, 92)( 72, 91)( 73, 90)( 74, 89)( 75, 88)( 76, 87)( 77, 86)( 78, 85)( 79, 84)( 80, 83)( 81, 82)( 93,116)( 94,138)( 95,137)( 96,136)( 97,135)( 98,134)( 99,133)(100,132)(101,131)(102,130)(103,129)(104,128)(105,127)(106,126)(107,125)(108,124)(109,123)(110,122)(111,121)(112,120)(113,119)(114,118)(115,117)(139,208)(140,230)(141,229)(142,228)(143,227)(144,226)(145,225)(146,224)(147,223)(148,222)(149,221)(150,220)(151,219)(152,218)(153,217)(154,216)(155,215)(156,214)(157,213)(158,212)(159,211)(160,210)(161,209)(162,254)(163,276)(164,275)(165,274)(166,273)(167,272)(168,271)(169,270)(170,269)(171,268)(172,267)(173,266)(174,265)(175,264)(176,263)(177,262)(178,261)(179,260)(180,259)(181,258)(182,257)(183,256)(184,255)(185,231)(186,253)(187,252)(188,251)(189,250)(190,249)(191,248)(192,247)(193,246)(194,245)(195,244)(196,243)(197,242)(198,241)(199,240)(200,239)(201,238)(202,237)(203,236)(204,235)(205,234)(206,233)(207,232); s1 := Sym(276)!( 1,163)( 2,162)( 3,184)( 4,183)( 5,182)( 6,181)( 7,180)( 8,179)( 9,178)( 10,177)( 11,176)( 12,175)( 13,174)( 14,173)( 15,172)( 16,171)( 17,170)( 18,169)( 19,168)( 20,167)( 21,166)( 22,165)( 23,164)( 24,140)( 25,139)( 26,161)( 27,160)( 28,159)( 29,158)( 30,157)( 31,156)( 32,155)( 33,154)( 34,153)( 35,152)( 36,151)( 37,150)( 38,149)( 39,148)( 40,147)( 41,146)( 42,145)( 43,144)( 44,143)( 45,142)( 46,141)( 47,186)( 48,185)( 49,207)( 50,206)( 51,205)( 52,204)( 53,203)( 54,202)( 55,201)( 56,200)( 57,199)( 58,198)( 59,197)( 60,196)( 61,195)( 62,194)( 63,193)( 64,192)( 65,191)( 66,190)( 67,189)( 68,188)( 69,187)( 70,232)( 71,231)( 72,253)( 73,252)( 74,251)( 75,250)( 76,249)( 77,248)( 78,247)( 79,246)( 80,245)( 81,244)( 82,243)( 83,242)( 84,241)( 85,240)( 86,239)( 87,238)( 88,237)( 89,236)( 90,235)( 91,234)( 92,233)( 93,209)( 94,208)( 95,230)( 96,229)( 97,228)( 98,227)( 99,226)(100,225)(101,224)(102,223)(103,222)(104,221)(105,220)(106,219)(107,218)(108,217)(109,216)(110,215)(111,214)(112,213)(113,212)(114,211)(115,210)(116,255)(117,254)(118,276)(119,275)(120,274)(121,273)(122,272)(123,271)(124,270)(125,269)(126,268)(127,267)(128,266)(129,265)(130,264)(131,263)(132,262)(133,261)(134,260)(135,259)(136,258)(137,257)(138,256); poly := sub<Sym(276)|s0,s1>;
Finitely Presented Group Representation (Magma)
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*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*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*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*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*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*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*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*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*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*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.