Uploaded September 2013 | Updated September 2026, 2 weeks ago
In Schwarz' D surface each chamber is connected to 4 neighboring ones with tunnels, in the I-WP surface (on one side at least) chambers are connected to 8 neighbors.
In the rhombic dodecahedron lattice, when observing the infinite version, a third of the chambers (in my build the spheres) is connected to 8 neighboring chambers that are all part of the remaining chambers that all have 4 connections to 4 chambers with 8 connections. In my build there are 3 types of chambers, in an infinite version a third is only connected with 4 narrow tunnels, another third only with 4 wide tunnels and the remaining third part has 4 wide and 4 narrow connections.
When leaving out all the spheres with narrow connections (and the narrow connections as well) then you get the D surface, when instead leaving out the ones with wide connections you also get the D surface. When adding a sphere in the center of each rhombic dodecahedron and connecting it with a wide tunnel to the 4 nearest spheres with narrow connections only and also with a narrow tunnel to the 4 nearest spheres with wide connections only, then you get Schwarz' I-WP surface.
In Schwarz' D surface each chamber is connected to 4 neighboring ones with tunnels, in the I-WP surface (on one side at least) chambers are connected to 8 neighbors.
In the rhombic dodecahedron lattice, when observing the infinite version, a third of the chambers (in my build the spheres) is connected to 8 neighboring chambers that are all part of the remaining chambers that all have 4 connections to 4 chambers with 8 connections. In my build there are 3 types of chambers, in an infinite version a third is only connected with 4 narrow tunnels, another third only with 4 wide tunnels and the remaining third part has 4 wide and 4 narrow connections.
When leaving out all the spheres with narrow connections (and the narrow connections as well) then you get the D surface, when instead leaving out the ones with wide connections you also get the D surface. When adding a sphere in the center of each rhombic dodecahedron and connecting it with a wide tunnel to the 4 nearest spheres with narrow connections only and also with a narrow tunnel to the 4 nearest spheres with wide connections only, then you get Schwarz' I-WP surface.
