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.
  • No picture means it's in my queue.
  • Non-clickable pictures still need me to write a description for them.

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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.

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

Stacks Image 1572

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

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

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

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

Seepferdchen
\( (x^2-y^3)^2 = (x+y^2)z^3 \)

Sofa
\( x^2+y^3+z^5 \)

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

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Wedeln
\( x^3=y(1-z^2)^2 \)

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

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Xano
\( x^3+z^3=yz^2 \)

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

Croissant
equation not given

Dromedar
\( x^4-3x^2+y^2+z^3 \)

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Zeppelin
\( xyz+yz+2z^5 \)

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

Michelangelo
\( x^2+y^4+y^3z^2 \)

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

Mobius
equation not given

Sphare
\( x^2+y^2+z^2=1 \)

Limao
\( x^2-y^3z^3 \)

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

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Whitney
\( x^2-y^2z \)

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

Zylinder
\( y^2+z^2=1 \)

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

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

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

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

Stacks Image 1861

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

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

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

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

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

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

Gupf
\( x^2+y^2+z \)

Kegel
\( x^2+y^2-z^2 \)

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

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

Pipe
\( x^2-z \)

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

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
\( x^2+y^2-z^3(1-z) =0 \)

Sattel
\( x^2+y^2z + z^3 = 0 \)

Schneeflocke
\( x^3+y^2z^3+yz^4 = 0 \)

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, and have posted medium and low resolution copies without watermark 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.