Lacing
Lacing is a general term describing the process of connecting two or more unconnected polytopes with additional, typically simpler, polytopes. This includes, but is not limited to: duopyramids, duoprisms, duotegums, (and normal prisms, pyramids, tegums) duocombs, antiprisms, cupolas, and lace prisms. Lacing may also appear describing the constructions of expansions, elongations, and gyroelongations.
Lacing may also remove the original laced polytopes like in many tegum products, and keep their facets, which then get connected.
Polytope | Tetrahedron | Hexagonal Prism | Pentagonal Tegum | Square Duocomb | Square Antiprism | Pentagonal Cupola |
---|---|---|---|---|---|---|
acronym | tet | hip | pet | squidic | squap | pecu |
description | duopyramid of two dyads | prism of a hexagon | duotegum of dyad and pentagon | duocomb of two squares | antiprism of a square | cupola of a pentagon |
original polytopes | 2 dyads | 2 hexagons | 1 dyad
1 pentagon |
4 squares | 2 squares | 1 pentagon
1 decagon |
lacing additions | 4 edges | 6 edges
6 squares |
removes dyad
removes pentagon 10 edges 10 triangles |
16 edges
16 squares |
8 edges | 10 edges
5 squares |
image |
Some polytopes have multiple ways to think of their lacings.
Polytope | Small Rhombicuboctahedron | Octahedron | Triangular-Square Duoprism | Snub Cube | |||||
---|---|---|---|---|---|---|---|---|---|
acronym | sirco | oct | tisdip | snic | |||||
description | expansion of cube | expansion of octahedron | elongated square orthobicupola | tegum of dyad and square | antiprism of triangle | duoprism of triangle and square | snubbed cube | snubbed octahedron | |
original polytopes | 6 squares | 8 triangles | 2 square cupolas | 1 dyad
1 square |
2 triangles | 4 triangles | 3 squares | 6 squares | 8 triangles |
lacing additions | 24 edges
12 squares |
24 edges
6 squares 12 squares |
removes octagons
8 edges 8 squares |
removes dyad
removes square 8 edges 12 triangles |
6 edges | 12 edges
3 squares 12 squares 4 trips 3 cubes |
12 edges
12 squares 4 trips 3 cubes |
24 edges
12 edges 24 triangles |
24 edges
12 edges 6 squares 24 triangles |
image |