C-P Family of Triply Periodic Minimal Surfaces

This family of triply periodic minimal surfaces is complementary to Schwartz' P surface. The kaleidoscopic cell is a quadrirectangular tetrahedron (1/48 of a cube) with a C2 symmetry axis.
Neovius kaleido Neovius surface

Neovius' Surface

A cubical unit cell, basically a central chamber with necks out to the middle of each edge of the cube. Genus 9.
Evolver file: neovius.fe

C15P kaleido Schoen C15(P) surface

Schoen's C15(P) Surface

The unit cell may be viewed as a chamber in a cube with tubes running to the centers of the faces and bracketing the centers of the edges. The unit cell has 96-fold symmetry (in the sense of having 96 copies of the fundamental region). This image was actually constructed by evolving the adjoint surface (which is in the datafile), adjusting a parameter to kill one period, and then doing an adjoint transformation. The name C15(P) refers to the surface being complementary to the P surface and having genus 15.
Evolver file: c15padj.fe

C21P kaleido Schoen C21(P) surface

Schoen's C21(P) Surface

The unit cell may be viewed as a chamber in a cube with tubes running to the centers of the edges and four tubes to each face. The unit cell has 96-fold symmetry (in the sense of having 96 copies of the fundamental region). This image was actually constructed by evolving the adjoint surface (which is in the datafile), adjusting a parameter to kill one period, and then doing an adjoint transformation. The name C21(P) refers to the surface being complementary to the P surface and having genus 21.
Evolver file: c21padj.fe

C27P kaleido Schoen C27(P) surface

Schoen's C27(P) Surface

Higher genus version in the sequence Neovius, C15P, C21P. The unit cell has 96-fold symmetry (in the sense of having 96 copies of the fundamental region). This image was actually constructed by evolving the adjoint surface (which is in the datafile), adjusting a parameter to kill two periods, and then doing an adjoint transformation. The name C27(P) refers to the surface being complementary to the P surface and having genus 27.
Evolver file: C27Padj.fe

C33P kaleido Schoen C33(P) surface

Schoen's C33(P) Surface

Higher genus version in the sequence Neovius, C15P, C21P, C27P. The unit cell has 96-fold symmetry (in the sense of having 96 copies of the fundamental region). This image was actually constructed by evolving the adjoint surface (which is in the datafile), adjusting a parameter to kill two periods, and then doing an adjoint transformation. The name C33(P) refers to the surface being complementary to the P surface and having genus 33.
Evolver file: C33Padj.fe,

C39P kaleido Schoen C39(P) surface

Schoen's C39(P) Surface

Higher genus version in the sequence Neovius, C15P, C21P, C27P, C33P. The unit cell has 96-fold symmetry (in the sense of having 96 copies of the fundamental region). This image was actually constructed by evolving the adjoint surface (which is in the datafile), adjusting a parameter to kill three periods, and then doing an adjoint transformation. The name C39(P) refers to the surface being complementary to the P surface and having genus 39.
Evolver file: C39Padj.fe

C45P kaleido Schoen C45(P) surface

Schoen's C45(P) Surface

Higher genus version in the sequence Neovius, C15P, C21P, C27P, C33P, C39P. The unit cell has 96-fold symmetry (in the sense of having 96 copies of the fundamental region). This image was actually constructed by evolving the adjoint surface (which is in the datafile), adjusting a parameter to kill three periods, and then doing an adjoint transformation. The name C45(P) refers to the surface being complementary to the P surface and having genus 45.
Evolver file: C45Padj.fe
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