nextstep
Site Admin
Joined: 06 Jan 2007
Posts: 539
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 Posted: Mon Sep 08, 2014 1:09 am Post subject: Sarti Dodecic (deg 12) |
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Hi all,
Sarti's dodecic surface of degree 12 was found during the writing of her Ph.D. thesis (advisor W. Barth) in 1999.
The Sarti surface is invariant under the bipolyhedral group and it has the symmetry of the 600-cell.
| Quote: | {
"Iso3D": {
"Cnd": [
"(x^2+y^2+z^2)>13"
],
"Component": [
"Sarti-Dodecic"
],
"Const": [
" w = 1.0"
],
"Fxyz": [
"243*(33*sqrt(5)*(((Ax*Ay+Az*w^2)^2*(Ax*Az+Ay*w^2)-(Ax*Ay+Az*w^2)*(Ax*Az+Ay*w^2)^2)+((Ax*Az+Ay*w^2)^2*(Ax*w^2+Ay*Az)-(Ax*Az+Ay*w^2)*(Ax*w^2+Ay*Az)^2)+((Ax*w^2+Ay*Az)^2*(Ax*Ay+Az*w^2)-(Ax*w^2+Ay*Az)*(Ax*Ay+Az*w^2)^2))+19*(((Ax*Ay+Az*w^2)^2*(Ax*Az+Ay*w^2)+(Ax*Ay+Az*w^2)*(Ax*Az+Ay*w^2)^2)+((Ax*Az+Ay*w^2)^2*(Ax*w^2+Ay*Az)+(Ax*Az+Ay*w^2)*(Ax*w^2+Ay*Az)^2)+((Ax*w^2+Ay*Az)^2*(Ax*Ay+Az*w^2)+(Ax*w^2+Ay*Az)*(Ax*Ay+Az*w^2)^2))+10*((Ax*Ay+Az*w^2)^3+(Ax*Az+Ay*w^2)^3+(Ax*w^2+Ay*Az)^3)-14*(Bx+By+Bz+w^4)*((Ax*Ay+Az*w^2)*(Ax*Az+Ay*w^2)+(Ax*Ay+Az*w^2)*(Ax*w^2+Ay*Az)+(Ax*Az+Ay*w^2)*(Ax*w^2+Ay*Az))+2*(Bx+By+Bz+w^4)^2*((Ax*Ay+Az*w^2)+(Ax*Az+Ay*w^2)+(Ax*w^2+Ay*Az))-6*(Bx+By+Bz+w^4)*((Ax*Ay+Az*w^2)^2+(Ax*Az+Ay*w^2)^2+(Ax*w^2+Ay*Az)^2)-352*(x*y*z*w)^2*((Ax*Ay+Az*w^2)+(Ax*Az+Ay*w^2)+(Ax*w^2+Ay*Az))+336*(x*y*z*w)^2*(Bx+By+Bz+w^4)+48*((Ax*Ay+Az*w^2)*(Ax*Az+Ay*w^2)*(Ax*w^2+Ay*Az)))-22*(Ax+Ay+Az+w^2)^6"
],
"Name": [
"SartiDodecic"
],
"Varu": [
" A = u^2",
" B = u^4"
],
"Xmax": [
"3.7"
],
"Xmin": [
"-3.7"
],
"Ymax": [
"3.7"
],
"Ymin": [
"-3.7"
],
"Zmax": [
"3.7"
],
"Zmin": [
"-3.7"
]
}
} |
 SartiDodecic by taha_ab, on Flickr
_________________
Cheers,
Abderrahman
Last edited by nextstep on Sat Sep 20, 2014 5:45 pm; edited 1 time in total |
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