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  • gifts
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  • materials
    • strong and flexible
    • multiple color sandstone
    • precious metal
    • steel
  • people
    • A-F
      • Werner Boy
      • Arthur Cayley
      • Alfred Clebsch
    • G-K
      • Olaus Henrici
      • Felix Klein
      • Ernst Eduard Kummer
    • L-R
      • August Ferdinand Möbius
      • Carl Rodenberg
    • S-Z
      • Ludwig Schläfli
      • Eugenio Giuseppe Togliatti
      • Christian Wiener
  • subjects
    • algebraic geometry
      • cubic surfaces
        • Clebsch Diagonal Surface
      • quartic surfaces
      • quintic surface
      • sextic surface
      • discriminant surfaces
      • many singularities
    • differential geometry
      • curvature
      • constant-curvature
      • Minimal Surfaces
    • school math
      • 3d-graph
      • surface of revolution
    • space curves
      • algebraic space curve
      • sine / cosine based curves
    • topology
      • non-orientable surfaces
      • knots
  • series
    • math sculptures in context
    • speed curves series
    • 45 cubics series I (ball cut)
    • 45 cubics series II (cylinder cut)
  • in public
    • exhibits
      • exhibit “3d print studio” (Feb. 2017-)
      • exhibit “Forms and Formulas” (2012-16)
      • exhibit at “Dutch Math Days” (2016)
    • articles.books
      • article “Straight lines on models of curved surfaces” (2017)
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  • Clebsch 27 lines only - a MO-Labs sculpture on math-sculpture.com
    The Clebsch diagonal surface: 27 lines only
    Gallery

    The Clebsch diagonal surface: 27 lines only

The Clebsch diagonal surface: 27 lines only

The sculpture we present here is a 3D-printed modern object consisting of the 27 lines only, and a thin part of the surface as a border.

Oliver Labs 2017-03-27T09:14:04+00:00 Alfred Clebsch, all, Clebsch Diagonal Surface, strong and flexible|
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  • Clebsch diagonal surface with colored double six
    The Clebsch diagonal surface with colored lines
    Gallery

    The Clebsch diagonal surface with colored lines

The Clebsch diagonal surface with colored lines

This version of Clebsch's famous diagonal surface model features colored lines. One intersects the surfaces in a line and a hyperbola, the another one in three lines.

Oliver Labs 2017-03-27T09:15:45+00:00 Alfred Clebsch, all, Carl Rodenberg, Clebsch Diagonal Surface, for mathematicians, Ludwig Schläfli, multiple color sandstone|
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  • symmetric cubic with 27 lines - a MO-Labs model from Math-Sculpture.com
    Tetrahedral symmetric cubic
    Gallery

    Tetrahedral symmetric cubic

Tetrahedral symmetric cubic

Cubic surfaces are classics from the 19th century. This particular cubic is smooth and has tetrahedral symmetry. All 27 lines are real, but only 24 are visible in the model because 3 are infinitly far away.

Oliver Labs 2017-03-27T10:49:26+00:00 all, cubic surfaces, strong and flexible|
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  • Clebsch diagonal surface with two planes
    The Clebsch diagonal surface with two planes
    Gallery

    The Clebsch diagonal surface with two planes

The Clebsch diagonal surface with two planes

This version of Clebsch's famous diagonal surface model features colored lines and two additional planes. One intersects the surfaces in a line and a hyperbola, the another one in three lines.

Oliver Labs 2017-03-27T09:09:53+00:00 Alfred Clebsch, all, article "Straight lines on models of curved surfaces" (2017), Clebsch Diagonal Surface, for mathematicians, multiple color sandstone|
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  • Clebsch diagonal surface in the family room
    The Clebsch diagonal surface in the family room
    Gallery

    The Clebsch diagonal surface in the family room

The Clebsch diagonal surface in the family room

Our modern version of Clebsch's historical - nowadays quite famous - diagonal surface model is the main figure in our photo from the series "math sculptures in context". It is the pure white version with the 27 straight lines.

Oliver Labs 2017-08-28T11:49:01+00:00 Alfred Clebsch, all, article "Straight lines on models of curved surfaces" (2017), Carl Rodenberg, Clebsch Diagonal Surface, for mathematicians, math sculptures in context, strong and flexible|
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Recent Posts

  • A Quintic with 15 Cusps
  • 45 cubics, series II (cylinder cut), 15cm
  • A gyroid, round cut
  • Moebius Strip ring
  • Moebius Strip pendant

Tags

27 lines 45 cubics algebraic curve algebraic surface brass classics classification Clebsch color colored lines cubic surface curvature cusp diagonal surface differential geometry double six gold gold plated in a cube jewelry knot mean curvature metal minimal surface modern classics Moebius Moebius strip Möbius one-sided one edge parabola pendant projection school sculpture silver singular singularities singularity smoothed space curve straight lines symmetry topology world record surface

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