Lacing

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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

4 triangles

6 edges

6 squares

removes dyad

removes pentagon

10 edges

10 triangles

16 edges

16 squares

8 edges

8 triangles

10 edges

5 triangles

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

8 triangles

12 squares

24 edges

6 squares

12 squares

removes octagons

8 edges

8 squares

removes dyad

removes square

8 edges

12 triangles

6 edges

6 triangles

12 edges

3 squares

12 squares

4 trips

3 cubes

12 edges

4 triangles

12 squares

4 trips

3 cubes

24 edges

12 edges

8 triangles

24 triangles

24 edges

12 edges

6 squares

24 triangles

image