Acronym | ... |
Name |
pentagonal double antitegmoid, pentaantitegmatoswirlic hectochoron, dual of great antiprism |
© | |
Circumradius | ... |
Vertex figure | tet, p2p5p |
Lace city in approx. ASCII-art |
o5o o5o o5F o5F F5o F5o o5o f5f f5f o5o F5x F5o F5o x5F x5F f5f f5f o5F o5F F5x F5x o5F o5F o5o f5f F5F f5f o5o F5o F5o x5F x5F F5o F5o f5f f5f F5x F5x o5F o5F x5F o5o f5f f5f o5o o5F o5F F5o F5o o5o o5o |
Dihedral angles |
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Dual | gap |
Face vector | 320, 720, 500, 100 |
Confer |
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External links |
The cells can also be obtained as a stellation of doe by blending at 2 neighbouring pentagons with tall pyramids, which are the tips of sissid and then inserting inbetween a wedge type simplex, as is used for gad.
The faces are regular pentagons of side v = (sqrt(5)-1)/2 = 0.618034; kites {(k,K,K,K)} with corner angle k = 36° and K = 108°, where side KK has size v again, diagonal KK has size x = 1, side kK has size f = (1+sqrt(5))/2 = 1.618034, and the diagonal kK has size sqrt[(5+sqrt(5))/2] = 1.902113; and trapzia {(t,t,T,T)} with corner angle t = 72° and T = 108°, where the side TT has size v again, while the other sides tT and tt have both size f again.
Incidence matrix according to Dynkin symbol
of|foxfv-5-of|ofxvf-2-fo|fvxof-5-fo|vfxfo-&#z(f,v) → existing heights = 0, lacing(1,3) = lacing(1,4) = lacing(2,6) = lacing(2,7) = f lacing(3,5) = lacing(4,5) = lacing(5,6) = lacing(6,7) = v o. ..... 5 o. ..... 2 o. ..... 5 o. ..... | 10 * * * * * * ♦ 1 1 5 5 0 0 0 0 0 0 0 0 0 0 0 0 | 5 5 10 0 0 0 0 0 0 0 | 5 5 0 0 .o ..... 5 .o ..... 2 .o ..... 5 .o ..... | * 10 * * * * * ♦ 0 0 0 0 1 1 5 5 0 0 0 0 0 0 0 0 | 0 0 0 5 5 10 0 0 0 0 | 0 0 5 5 .. o.... 5 .. o.... 2 .. o.... 5 .. o.... | * * 50 * * * * ♦ 0 0 1 0 0 0 0 0 1 2 0 0 0 0 0 0 | 1 0 2 0 0 0 2 1 0 0 | 1 2 1 0 .. .o... 5 .. .o... 2 .. .o... 5 .. .o... | * * * 50 * * * ♦ 0 0 0 1 0 0 0 0 0 0 1 2 0 0 0 0 | 0 1 2 0 0 0 0 0 2 1 | 2 1 0 1 .. ..o.. 5 .. ..o.. 2 .. ..o.. 5 .. ..o.. | * * * * 100 * * ♦ 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 | 0 0 1 0 0 1 1 1 1 1 | 1 1 1 1 .. ...o. 5 .. ...o. 2 .. ...o. 5 .. ...o. | * * * * * 50 * ♦ 0 0 0 0 0 0 1 0 0 0 0 0 2 0 1 0 | 0 0 0 1 0 2 0 2 1 0 | 1 0 2 1 .. ....o 5 .. ....o 2 .. ....o 5 .. ....o | * * * * * * 50 ♦ 0 0 0 0 0 0 0 1 0 0 0 0 0 2 0 1 | 0 0 0 0 1 2 1 0 0 2 | 0 1 1 2 --------------------------------------------------+-----------------------+-------------------------------------------------+---------------------------------+------------ .. ..... .. ..... f. ..... .. ..... | 2 0 0 0 0 0 0 | 5 * * * * * * * * * * * * * * * | 0 5 0 0 0 0 0 0 0 0 | 5 0 0 0 f .. ..... .. ..... .. ..... f. ..... | 2 0 0 0 0 0 0 | * 5 * * * * * * * * * * * * * * | 5 0 0 0 0 0 0 0 0 0 | 0 5 0 0 f o. o.... 5 o. o.... 2 o. o.... 5 o. o....&#f | 1 0 1 0 0 0 0 | * * 50 * * * * * * * * * * * * * | 1 0 2 0 0 0 0 0 0 0 | 1 2 0 0 f o. .o... 5 o. .o... 2 o. .o... 5 o. .o...&#f | 1 0 0 1 0 0 0 | * * * 50 * * * * * * * * * * * * | 0 1 2 0 0 0 0 0 0 0 | 2 1 0 0 f .f ..... .. ..... .. ..... .. ..... | 0 2 0 0 0 0 0 | * * * * 5 * * * * * * * * * * * | 0 0 0 0 5 0 0 0 0 0 | 0 0 0 5 f .. ..... .f ..... .. ..... .. ..... | 0 2 0 0 0 0 0 | * * * * * 5 * * * * * * * * * * | 0 0 0 5 0 0 0 0 0 0 | 0 0 5 0 f .o ...o. 5 .o ...o. 2 .o ...o. 5 .o ...o.&#f | 0 1 0 0 0 1 0 | * * * * * * 50 * * * * * * * * * | 0 0 0 1 0 2 0 0 0 0 | 0 0 2 1 f .o ....o 5 .o ....o 2 .o ....o 5 .o ....o&#f | 0 1 0 0 0 0 1 | * * * * * * * 50 * * * * * * * * | 0 0 0 0 1 2 0 0 0 0 | 0 0 1 2 f .. ..... .. ..... .. ..... .. v.... | 0 0 2 0 0 0 0 | * * * * * * * * 25 * * * * * * * | 1 0 0 0 0 0 2 0 0 0 | 0 2 1 0 v .. o.o.. 5 .. o.o.. 2 .. o.o.. 5 .. o.o..&#v | 0 0 1 0 1 0 0 | * * * * * * * * * 100 * * * * * * | 0 0 1 0 0 0 1 1 0 0 | 1 1 1 0 v .. ..... .. ..... .. .v... .. ..... | 0 0 0 2 0 0 0 | * * * * * * * * * * 25 * * * * * | 0 1 0 0 0 0 0 0 2 0 | 2 0 0 1 v .. .oo.. 5 .. .oo.. 2 .. .oo.. 5 .. .oo..&#v | 0 0 0 1 1 0 0 | * * * * * * * * * * * 100 * * * * | 0 0 1 0 0 0 0 0 1 1 | 1 1 0 1 v .. ..oo. 5 .. ..oo. 2 .. ..oo. 5 .. ..oo.&#v | 0 0 0 0 1 1 0 | * * * * * * * * * * * * 100 * * * | 0 0 0 0 0 1 0 1 1 0 | 1 0 1 1 v .. ..o.o 5 .. ..o.o 2 .. ..o.o 5 .. ..o.o&#v | 0 0 0 0 1 0 1 | * * * * * * * * * * * * * 100 * * | 0 0 0 0 0 1 1 0 0 1 | 0 1 1 1 v .. ..... .. ...v. .. ..... .. ..... | 0 0 0 0 0 2 0 | * * * * * * * * * * * * * * 25 * | 0 0 0 1 0 0 0 2 0 0 | 1 0 2 0 v .. ....v .. ..... .. ..... .. ..... | 0 0 0 0 0 0 2 | * * * * * * * * * * * * * * * 25 | 0 0 0 0 1 0 0 0 0 2 | 0 1 0 2 v --------------------------------------------------+-----------------------+-------------------------------------------------+---------------------------------+------------ .. ..... .. ..... .. ..... f. v....&#f | 2 0 2 0 0 0 0 | 0 1 2 0 0 0 0 0 1 0 0 0 0 0 0 0 | 25 * * * * * * * * * | 0 2 0 0 {(k,K,K,K)} .. ..... .. ..... f. .v... .. .....&#f | 2 0 0 2 0 0 0 | 1 0 0 2 0 0 0 0 0 0 1 0 0 0 0 0 | * 25 * * * * * * * * | 2 0 0 0 {(k,K,K,K)} o. ooo.. 5 o. ooo.. 2 o. ooo.. 5 o. ooo..&#r(f,v) | 1 0 1 1 1 0 0 | 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 | * * 100 * * * * * * * | 1 1 0 0 {(t,t,T,T)}, cycle: (acfe) .. ..... .f ...v. .. ..... .. .....&#f | 0 2 0 0 0 2 0 | 0 0 0 0 0 1 2 0 0 0 0 0 0 0 1 0 | * * * 25 * * * * * * | 0 0 2 0 {(k,K,K,K)} .f ....v .. ..... .. ..... .. .....&#f | 0 2 0 0 0 0 2 | 0 0 0 0 1 0 0 2 0 0 0 0 0 0 0 1 | * * * * 25 * * * * * | 0 0 0 2 {(k,K,K,K)} .o ..ooo 5 .o ..ooo 2 .o ..ooo 5 .o ..ooo&#r(f,v) | 0 1 0 0 1 1 1 | 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 | * * * * * 100 * * * * | 0 0 1 1 {(t,t,T,T)}, cycle: (bfeg) .. ..... .. ..... .. ..... .. v.x.o&#vt | 0 0 2 0 2 0 1 | 0 0 0 0 0 0 0 0 1 2 0 0 0 2 0 0 | * * * * * * 50 * * * | 0 1 1 0 v-{5} .. ..... .. o.xv. .. ..... .. .....&#vt | 0 0 1 0 2 2 0 | 0 0 0 0 0 0 0 0 0 2 0 0 2 0 1 0 | * * * * * * * 50 * * | 1 0 1 0 v-{5} .. ..... .. ..... .. .vxo. .. .....&#vt | 0 0 0 2 2 1 0 | 0 0 0 0 0 0 0 0 0 0 1 2 2 0 0 0 | * * * * * * * * 50 * | 1 0 0 1 v-{5} .. .ox.v .. ..... .. ..... .. .....&#vt | 0 0 0 1 2 0 2 | 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 1 | * * * * * * * * * 50 | 0 1 0 1 v-{5} --------------------------------------------------+-----------------------+-------------------------------------------------+---------------------------------+------------ .. ..... o. ofxv. f. fvxo. .. .....&#(f,v)t ♦ 2 0 2 4 4 2 0 | 1 0 2 4 0 0 0 0 0 4 2 4 4 0 1 0 | 0 2 4 0 0 0 0 2 2 0 | 25 * * * tower: a-d-c-e-f o. fox.v .. ..... .. ..... f. vfx.o&#(f,v)t ♦ 2 0 4 2 4 0 2 | 0 1 4 2 0 0 0 0 2 4 0 4 0 4 0 1 | 2 0 4 0 0 0 2 0 0 2 | * 25 * * tower: a-c-d-e-g .. ..... .f o.xvf .. ..... .o v.xfo&#(f,v)t ♦ 0 2 2 0 4 4 2 | 0 0 0 0 0 1 4 2 1 4 0 0 4 4 2 0 | 0 0 0 2 0 4 2 2 0 0 | * * 25 * tower: b-f-g-e-c .f .oxfv .. ..... .o .vxof .. .....&#(f,v)t ♦ 0 2 0 2 4 2 4 | 0 0 0 0 1 0 2 4 0 0 1 4 4 4 0 2 | 0 0 0 0 2 4 0 0 2 2 | * * * 25 tower: b-g-f-e-d
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