Author Message
nextstep

Joined: 06 Jan 2007
Posts: 539

Posted: Fri Sep 05, 2014 4:28 am    Post subject: Endraß octic (deg 8)

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
nextstep

Joined: 06 Jan 2007
Posts: 539

Posted: Sat Sep 20, 2014 11:28 pm    Post subject: Sarti's Octic

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
 Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year Oldest FirstNewest First
 All times are GMT Page 1 of 1

 Jump to: Select a forum MathMod----------------MathMod Progress & featuresMathematical Models CollectionHow toBugsMathMod for WindowsMathMod for Linux/UnixMathMod For MACOSXMathMod TutorialsOther Mathematical ToolsOpen Discussion K3DSurf----------------K3DSurf Discuss/DiscussionsHow toK3DSurf math related questionsK3DSurf for WindowsK3DSurf for MacOSK3DSurf for LinuxOnline K3DSurf: J3DSurfNewsBugsOnline DocumentationAccount Activation Issue ?/ Problème d'activation de votre compte ?
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