Endraß octic (deg 8)

 
Post new topic   Reply to topic    K3DSurf forum Forum Index -> Mathematical Models Collection
View previous topic :: View next topic  
Author Message
nextstep
Site Admin


Joined: 06 Jan 2007
Posts: 538

PostPosted: Fri Sep 05, 2014 4:28 am    Post subject: Endraß octic (deg 8) Reply with quote

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
Back to top View user's profile Send private message
nextstep
Site Admin


Joined: 06 Jan 2007
Posts: 538

PostPosted: Sat Sep 20, 2014 11:28 pm    Post subject: Sarti's Octic Reply with quote

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"
]
}
}

SartiOctic by taha_ab, on Flickr
_________________
Cheers,
Abderrahman
Back to top View user's profile Send private message
Display posts from previous:   
Post new topic   Reply to topic    K3DSurf forum Forum Index -> Mathematical Models Collection All times are GMT
Page 1 of 1

 
Jump to:  
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum


2005 Powered by phpBB © 2001, 2005 phpBB Group


Start Your Own Video Sharing Site

Free Web Hosting | Free Forum Hosting | FlashWebHost.com | Image Hosting | Photo Gallery | FreeMarriage.com

Powered by PhpBBweb.com, setup your forum now!
For Support, visit Forums.BizHat.com