Hauser's Algebraic Surface Gallery

Reproductions in 3D of Herwig Hauser's fine raytraced surfaces, using real numerical cellular decomposition implemented in Bertini_real

  • Regarding how I printed these models, I have some advice here.
  • Click on the pictures to find out more about the surfaces.
  • Non-clickable pictures still need me to write a description for them. These are indicated with a ° next to the name of the surface.

Herwig Hauser gallery medley of 3d printed algebraic surfaces Tobel, Croissant, Kreuz, Stern
14 of the 72 remain to be printed as of July 2018. Many have been printed but not yet photographed or documented. This turned out to be a long project! I started it (informally) as I started implementing the surface decomposition routine of Bertini_real in Fall 2013. Each surface takes 15-30 minutes to writeup and post, and there's also the computation time, post-processing to make it printable, and print time. This project is truly a labor of love. I thank those who have helped me with it over the years.

Calyx
\(x^2+y^2 z^3 = z^4\)

Calypso
\(x^2+y^2 z = z^2\)

Columpius
\(x^3y + xz^3 +y^3z + z\)
\( + 7z^2 + 5z\)

Cube
\(x^6+y^6+z^6 = 1\)

Dattel °
\(3x^2+3y^2+z^2=1\)

Daisy °
\((x^2-y^3)^2 = (z^2-y^2)^3\)

Dingdong
\(x^2+y^2+z^3=z^2\)

Distel
\(x^2+y^2+z^2 + 1000(x^2+y^2) \)
\((x^2+z^2)(y^2+z^2) = 1\)

Durchblick
\( x^3 y+ xz^3 +y^3z+z^3+5z \)

Eistute °
\( (x^2+y^2)^3 = 4x^2y^2(z^2+1) \)

eistute_thumbnail

Eve
\( \frac{1}{2}x^2+2xz^2+5y^6+15y^4+\frac{1}{2}z^2 = 15y^5 +5y^3 \)

Flirt °
\( x^2-x^3+y^2+y^4+z^3-10z^ 4 \)

flirt_thumbnail

Geisha
\( x^2yz+x^2z^2 = y^3z+y^3 \)

Harlekin °
\(x^3z+10x^2y+xy^2+yz^2 = z^3 \)

Helix
\( 6x^2-2x^4 = y^2z^2 \)

Herz °
\( y^2+z^3-z^4-x^2z^2 \)

Himmel und Holle
\( x^2-y^2z^2 \)

Kolibri
\( x^3+x^2z^2 - y^2 \)

Leopold
\( 1000 x^2y^2z^2 + 3x^2+3y^2+z^2=1 \)

Octdong °
\( x^2+y^2+z^4 = z^2 \)

octdong_thumb

Plop
\( x^2 + (z+y^2)^3 \)

Seepferdchen
\( x^4-2.5x^2y^3 -xz^3 +y^6 -y^2z^3 \)

Sofa °
\( x^2+y^3+z^5 \)

sofa_thumb

Solitude
\( x^2yz+xy^2+y^3+y^3z = x^2z^2 \)

Suss
\( (x^2+\frac{9}{4}y^2 + z^2-1)^3 - x^2z^3 - \)
\( \frac{9}{80}y^2z^3 \)

Tanz °
\( x^4-x^2-y^2z^2 \)

Taube °
\( 256z^3-128x^2z^2+16x^4z \)
\( +144 xy^2z-4x^3y^2-27y^4 \)

Quaste °
equation not given

Spitz °
\( (y^3-x^2-z^2)^3 = 27x^2y^3z^2 \)

Tobel
\( x^3z+x^2+yz^3+z^4 = 3xyz \)

Vis a vis °
\( x^2-x^3+y^2+y^4+z^3-z^4 \)

vis_a_vis_thumb

Wedeln °
\( x^3=y(1-z^2)^2 \)

wedeln_thumb

Windkanal °
\( -x^2+y^4+z^4-xyz = 100 \)

windkanal_thumb

Xano °
\( x^3+z^3=yz^2 \)

xano_thumb

Zitrus °
\( x^2+z^2+y^3(y-1)^3 \)

zitrus_thumb

Croissant °
equation not given

Dromedar °
\( x^4-3x^2+y^2+z^3 \)

dromedar_thumb

Zeppelin °
\( xyz+yz+2z^5 \)

Zweiloch °
\( x^3y+xz^3+y^3z + z^3+7z^2+5z \)

Michelangelo °
\( x^2+y^4+y^3z^2 \)

michelangelo_thumb

Stern °
\( 400(x^2y^2+y^2z^2 +x^2z^2) + (x^2+y^2+z^2 -1)^3 \)

stern_thumb

Mobius °
equation not given

Sphare °
\( x^2+y^2+z^2=1 \)

sphere_thumb

Limao °
\( x^2-y^3z^3 \)

limao_thumb

Torus °
\( (x^2+y^2\)
\( +z^2+R^2-r^2)^2 \)
\( = R^2(x^2+y^2) \)

torus_thumb

Whitney °
\( x^2-y^2z \)

whitney_thumb

Buggle °
\( x^4y^2+y^4x^2-x^2y^2 + z^6 \)

buggle_thumb

Zylinder °
\( y^2+z^2=1 \)

Diabolo °
\( x^2=(y^2+z^2)^2 \)

Dullo °
\( (x^2+y^2+z^2)^2\)
\( -(x^2+y^2) \)

dullo_thumb

Miau °
\( x^2yz+x^2z^2\)
\( +2y^3z+3y^3 \)

miao_thumb

Trichter °
\( x^2+z^3 \)
\( = y^2z^2 \)

trichter_thumb

Nepali °
\( (xy-z^3-1)^2 + (x^2+y^2-1)^3 \)

nepali_thumb

Pilzchen °
\( (z^3-1)^2+(x^2+y^2-1)^3 \)

pilzchen_thumb

Subway °
\( x^2y^2+(z^2-1)^3 \)

subway_thumb

Polsterzipf
\( (x^3-1)^2+(y^3-1)^2+(z^2-1)^3 \)

Crixxi °
\( (y^2+z^2-1)^2 \)
\(+ (x^2+y^2-1)^3 \)

crixxi_thumb

Berg °
\( x^2+y^2z^2 + z^3 \)

Gupf °
\( x^2+y^2+z \)

Kegel °
\( x^2+y^2-z^2 \)

kegel_thumb

Wigwam
\( x^2+y^2z^3 \)

Tuelle
\( yz(x^2+y-z) \)

Pipe °
\( x^2-z \)

Fanfare °
\( -x^3+z^2+y^2 \)

fanfare_thumb

Kreuz
\( xyz \)

Spindel
\( x^2+y^2-z^2=1 \)

Twilight
\( (z^3-2)^2+\)
\((x^2+y^2-3)^3 \)

Ufo °
\( z^2-x^2-y^2=1 \)

Wendel °
equation not given

Zeck
\( x^2+y^2-z^3(1-z)\)

Sattel
\( x^2+y^2z + z^3\)

Schneeflocke °
\( x^3+y^2z^3+yz^4\)

I currently do the photography using a nylon photo booth, some spotlights, and a Canon Rebel xsi camera. If you identify ways for me to improve my photography, please email me and share! I want to take the best pictures I can possibly produce, and welcome the advice of others!

© I own the copyright to all of these images.

I have posted * low-res thumbnails on the main page, and medium quality copies without watermark on the focused pages, as a service to the mathematical and broader community. I retain all originals -- if you would like to use an original for a publication, please email me.