Triply Periodic Minimal Surfaces - Disphenoid Surfaces

This page presents several families of triply periodic minimal surfaces that have the tetragonal disphenoid as their kaleidoscopic cell, with short and long C2 symmetry axes.

Note: What is referred to below as a "unit cell" is a unit cell for the unoriented surface; the oriented unit cell is twice as big.


disphenoid p=3 disphenoid p=3 cubelet disphenoid p=3 cube disphenoid p=3 rhombic

Schwartz' D surface - genus 3

At left is four fundamental regions in a disphenoid, with two C2 axes. At mid left, twelve fundamental regions form a cubelet. At mid right is a cubic unit cell formed from four cubelets. At right is a rhombic dodecahedron made of 24 disphenoids.
Evolver file: dcell.fe


Family A

This family progressively introduces a new edge along the long side of the disphenoid.
disphenoid p=19 disphenoid p=19 cubelet disphenoid p=19 cube disphenoid p=19 rhombic

Schoen's complementary D surface - genus 19

At left is four fundamental regions in a disphenoid, with two C2 axes. At mid left, twelve fundamental regions form a cubelet. At mid right is a cubic unit cell formed from four cubelets. At right is a rhombic dodecahedron made of 24 disphenoids.
Evolver file: disphenoid19.fe

disphenoid p=31 disphenoid p=31 cubelet disphenoid p=31 cube disphenoid p=31 rhombic

New disphenoid surface - genus 31

At left is four fundamental regions in a disphenoid, with two C2 axes. At mid left, twelve fundamental regions form a cubelet. At mid right is a cubic unit cell formed from four cubelets. At right is a rhombic dodecahedron made of 24 disphenoids.
Evolver file: disphenoid31adj.fe

disphenoid p=43 disphenoid p=43 cubelet disphenoid p=43 cube disphenoid p=43 rhombic

New disphenoid surface - genus 43

The next member in the family of the previous surface. At left is four fundamental regions in a disphenoid, with two C2 axes. At mid left, twelve fundamental regions form a cubelet. At mid right is a cubic unit cell formed from four cubelets. At right is a rhombic dodecahedron made of 24 disphenoids.
Evolver file: disphenoid43adj.fe

disphenoid p=55 disphenoid p=55 cubelet disphenoid p=55 cube disphenoid p=55 rhombic

New disphenoid surface - genus 55

The next member in the family of the previous surface. At left is four fundamental regions in a disphenoid, with two C2 axes. At mid left, twelve fundamental regions form a cubelet. At mid right is a cubic unit cell formed from four cubelets. At right is a rhombic dodecahedron made of 24 disphenoids.
Evolver file: disphenoid55adj.fe


Family B

This family progressively introduces a new edge along the short side of the disphenoid.
disphenoid p=19 disphenoid p=19 cubelet disphenoid p=19 cube disphenoid p=19 rhombic

Schoen's complementary D surface - genus 19

At left is four fundamental regions in a disphenoid, with two C2 axes. At mid left, twelve fundamental regions form a cubelet. At mid right is a cubic unit cell formed from four cubelets. At right is a rhombic dodecahedron made of 24 disphenoids.
Evolver file: disphenoid19.fe

disphenoid p=35 disphenoid p=35 cubelet disphenoid p=35 cube disphenoid p=35 rhombic

New disphenoid surface - genus 35

At left is four fundamental regions in a disphenoid, with two C2 axes. At mid left, twelve fundamental regions form a cubelet. At mid right is a cubic unit cell formed from four cubelets. At right is a rhombic dodecahedron made of 24 disphenoids.
Evolver file: disphenoid35adj.fe

disphenoid p=51 disphenoid p=51 cubelet disphenoid p=51 cube disphenoid p=51 rhombic

New disphenoid surface - genus 51

At left is four fundamental regions in a disphenoid, with two C2 axes. At mid left, twelve fundamental regions form a cubelet. At mid right is a cubic unit cell formed from four cubelets. At right is a rhombic dodecahedron made of 24 disphenoids.
Evolver file: disphenoid51adj.fe

disphenoid p=67 disphenoid p=67 cubelet disphenoid p=67 cube disphenoid p=67 rhombic

New disphenoid surface - genus 67

At left is four fundamental regions in a disphenoid, with two C2 axes. At mid left, twelve fundamental regions form a cubelet. At mid right is a cubic unit cell formed from four cubelets. At right is a rhombic dodecahedron made of 24 disphenoids.
Evolver file: disphenoid67adj.fe


Back to Triply Periodic Minimal Surfaces.
Back to Ken Brakke's home page.
Susquehanna University assumes no responsibility for the content of this personal Web page. Please read the disclaimer.