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nextstep Site Admin
Joined: 06 Jan 2007 Posts: 539
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Posted: Fri Sep 05, 2014 4:28 am Post subject: Endraß octic (deg 8) |
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Hi all,
Endraß surfaces are a pair of octic surfaces which have 168 ordinary double points. This is the maximum number known to exist for an octic surface, although the rigorous upper bound is 174.
Endraß constructed it in 1997 during the writing of his Ph.D. thesis (advisor W. Barth).
The surfaces were discovered in a five-dimensional family of octics with 112 nodes.
The illustrated surface take w=1 and has 144 real ordinary double points.
Code: | {
"Iso3D": {
"Cnd": [
"(x^2+y^2+z^2)>25"
],
"Component": [
"Endraß-Octic"
],
"Const": [
" w = 1.0",
"a1 = 1.0",
"a2 = 1.0",
"a3 = 1.0",
"a4 = -1.0"
],
"Fxyz": [
"64 * (x^2 - w^2)*(y^2 - w^2)*((x + y)^2 -2*w^2)*((x - y)^2 -2*w^2) - (-4*(1 + a1*2^(1/2))*(x^2 + y^2)^2 +
(8*(2 + a2*2^(1/2))*z^2 + 2*(2 + a3*7*2^(1/2))*w^2 )* (x^2 + y^2) -
16*z^4+ 8*(1 + a4*2*2^(1/2))*z^2*w^2 - (1 + 12*2^(1/2))*w^4)^2"
],
"Name": [
"Endraß-Octic"
],
"Xmax": [
"5"
],
"Xmin": [
"-5"
],
"Ymax": [
"5"
],
"Ymin": [
"-5"
],
"Zmax": [
"5"
],
"Zmin": [
"-5"
]
}
} |
EndraßOctic by taha_ab, on Flickr _________________ Cheers,
Abderrahman |
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nextstep Site Admin
Joined: 06 Jan 2007 Posts: 539
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Posted: Sat Sep 20, 2014 11:28 pm Post subject: Sarti's Octic |
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Hi all,
This is the Alessandra Sarti's Octic version with 144 nodes (see also her Dodecic (deg 12) 600 nodes)
Quote: | {
"Iso3D": {
"Component": [
" SartiOctic"
],
"Fxyz": [
"-1728*x^4*y^2*z^2+928.0*z^4*x^4+9024.0*z^2*x^4+928.0*z^4*y^4+9024.0*z^2*y^4+9024.0*x^2*y^2+2720.0*x^4*y^4-1728*x^2*z^2-1728*y^2*z^2-1728*x^4*y^2-1728*x^2*y^4-1728*x^2*z^4-1728*y^2*z^4-576*x^6*y^2-576*x^6*z^2-576*x^2*y^6-576*x^2*z^6-576*y^6*z^2+9024.0*z^4*x^2*y^2-24960.0*z^2*x^2*y^2-1728*x^2*y^4*z^2+2720.0*z^4+112.0*z^8-576*z^2+928.0*x^4+112.0*x^8+928.0*y^4+112.0*y^8-576*x^2-576*y^2-576*x^6-576*y^6-576*z^6+112.0-576*y^2*z^6"
],
"Name": [
"SartiOctic"
],
"Xmax": [
"5.6"
],
"Xmin": [
"-5.6"
],
"Ymax": [
"5.6"
],
"Ymin": [
"-5.6"
],
"Zmax": [
"5.6"
],
"Zmin": [
"-5.6"
]
}
}
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SartiOctic by taha_ab, on Flickr _________________ Cheers,
Abderrahman |
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