Schoen's Hybrid Triply Periodic Minimal Surfaces

This page presents several families of triply periodic minimal surfaces that may be viewed as combinations of other surfaces. A common way to conceptualize them is to view them as a central body in a polyhedron with tunnels extending out to various faces, edges, or vertices.

S'-S surface
S'-S"
The unit cell is a square box with tunnels to the top and bottom of the box and to the vertical edges. The box cannot be a cube; this shows the maximum height box in which the surface exists. For lower boxes, two surfaces exist, one with a narrower neck top and bottom and one with a wider neck. Genus 4.
Evolver file: SSadj.fe

P surface
P
Schwarz' P surface, included here for reference. The unit cell is a cube, and tunnels extend to each face. Genus 3.
Evolver file: pcell.fe

S'-S''|P surface
S'-S"|P
This surface can be viewed as S'-S" with P-type tunnels coming out of the top and bottom necks. Actually a 1-parameter family in the ratio of the sizes of the necks. Genus 6.
Evolver file: pssadj.fe

H'-T surface
H'-T
This surface may be viewed as narrow tunnels to the sides of a hexagonal prism, with wide tunnels to the top and bottom. Genus 4.
Evolver file: HTadj.fe

H''-R surface
H"-R
This surface may be viewed as narrow tunnels to the vertical edges of a hexagonal prism, with wide tunnels to the top and bottom. Genus 5.
Evolver file: HRadj.fe

T'-R' surface
T'-R'
This surface may be viewed as a central body with tunnels to the sides of a hexagonal prism, and those tunnels merged vertically. Genus 6.
Evolver file: TRadj.fe

H'-T|H''-R surface
H'-T|H"-R
A hexagonal prism with narrow tunnels to both vertical faces and vertical edges. Ratio of sizes of necks can be varied. Genus 8.
Evolver file: HRHTadj.fe

T'-R'|H'-T surface
T'-R'|H'-T
A central body in a hexagonal prism with tunnels out to the vertical faces, and those tunnels connected vertically. Or T'-R' with catenoid holes punched through certain places. Ratio of sizes of necks can be varied. Genus 9.
Evolver file: HTTRadj.fe

T'-R'|H''-R surface
H"-R|T'-R'
A central body in a hexagonal prism with tunnels out to the vertical edges, and those tunnels connected vertically. Ratio of sizes of necks can be varied. Genus 10.
Evolver file: TRHTadj.fe


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