The chamfered cube is constructed as a chamfer of a cube: the squares are reduced in size and new faces, hexagons, are added in place of all the original edges. The cC is a convex polyhedron with 32 vertices, 48 edges, and 18 faces: 6 congruent (and regular) squares, and 12 congruent flattened hexagons.For a certain depth of chamfering, all (final) edges of the chamfered cube have the same length; then, the hexagons are equilateral, but not regular. They are congruent alternately truncated rhombi, have 2 internal angles of cos − 1 ⁡ ( − 1 3 ) ≈ 109.47 ∘ {\displaystyle \cos ^{-1}(-{\frac {1}{3}})\approx 109.47^{\circ }} and 4 internal angles of π − 1 2 cos − 1 ⁡ ( − 1 3 ) ≈ 125.26 ∘ , {\displaystyle \pi -{\frac {1}{2}}\cos ^{-1}(-{\frac {1}{3}})\approx 125.26^{\circ },} while a regular hexagon would have all 120 ∘ {\displaystyle 120^{\circ }} internal angles.

Chamfer vs bevel

The truncated octahedron or truncated icosahedron, GP(1,1), creates a Goldberg sequence: GP(1,1), GP(2,2), GP(4,4), GP(8,8)...

How to pronounce chamfer

A truncated tetrakis hexahedron or pentakis dodecahedron, GP(3,0), creates a Goldberg sequence: GP(3,0), GP(6,0), GP(12,0)...

The cC is also inaccurately called a truncated rhombic dodecahedron, although that name rather suggests a rhombicuboctahedron. The cC can more accurately be called a tetratruncated rhombic dodecahedron, because only the (6) order-4 vertices of the rhombic dodecahedron are truncated.

Chamfered edge meaning

A topological equivalent to the chamfered cube, but with pyritohedral symmetry and rectangular faces, can be constructed by chamfering the axial edges of a pyritohedron. This occurs in pyrite crystals.

For a certain depth of chamfering/truncation, all (final) edges of the cT have the same length; then, the hexagons are equilateral, but not regular.

'Mill ends' are the surplus yardage of yarn produced by mills every time a production run ends. Most mills do not have storage space for this surplus, and the production overrun does not produce sufficient bulk quantity to interest most of their buyers; in the past, this has meant that mill ends represented waste that simply had to be thrown away. Tonnes of perfectly good fiber every year just tossed in a landfill, or sent to be shredded for fiberfill. Fortunately, a market for this surplus material has began to open up in recent years, with mills able to find smaller buyers that they can sell the ends to at a discounted price. That extra value can then be passed on to the customer - the end result being that consumers get cheaper yarn, small businesses have better opportunities for growth and mills don't have to throw out their mill ends. It should be emphasized that mill ends are no different in quality from the yarn run they came from! Buying mill ends is not buying an inferior product, just a product that has a difficult time finding a home. We've just finished adding our own mill end collection to our wholesale stock catalog, and would encourage you to browse through the selection.

In geometry, chamfering or edge-truncation is a topological operator that modifies one polyhedron into another. It is similar to expansion: it moves the faces apart (outward), and adds a new face between each two adjacent faces; but contrary to expansion, it maintains the original vertices. (Equivalently: it separates the faces by reducing them, and adds a new face between each two adjacent faces; but it only moves the vertices inward.) For a polyhedron, this operation adds a new hexagonal face in place of each original edge.

Chamfered edge

For polychora, new cells are created around the original edges. The cells are prisms, containing two copies of the original face, with pyramids augmented onto the prism sides.[something may be wrong in this passage]

Chamfer in AutoCAD

In Conway polyhedron notation, chamfering is represented by the letter "c". A polyhedron with e edges will have a chamfered form containing 2e new vertices, 3e new edges, and e new hexagonal faces.

Chamfer vs fillet

The cD is also inaccurately called a truncated rhombic triacontahedron, although that name rather suggests a rhombicosidodecahedron. The cD can more accurately be called a pentatruncated rhombic triacontahedron, because only the (12) order-5 vertices of the rhombic triacontahedron are truncated.

In the chapters below, the chamfers of the five Platonic solids are described in detail. Each is shown in an equilateral version where all edges have the same length, and in a canonical version where all edges touch the same midsphere. (They look noticeably different only for solids containing triangles.) The shown dual polyhedra are dual to the canonical versions.

In geometry, the chamfered octahedron is a convex polyhedron constructed by truncating the 8 order-3 vertices of the rhombic dodecahedron. These truncated vertices become congruent equilateral triangles, and the original 12 rhombic faces become congruent flattened hexagons.For a certain depth of truncation, all (final) edges of the cO have the same length; then, the hexagons are equilateral, but not regular.

Chamfer Tool

In geometry, the chamfered icosahedron is a convex polyhedron constructed by truncating the 20 order-3 vertices of the rhombic triacontahedron. The hexagonal faces of the cI can be made equilateral, but not regular, with a certain depth of truncation.

The chamfered dodecahedron is a convex polyhedron with 80 vertices, 120 edges, and 42 faces: 12 congruent regular pentagons and 30 congruent flattened hexagons.It is constructed as a chamfer of a regular dodecahedron. The pentagons are reduced in size and new faces, flattened hexagons, are added in place of all the original edges. For a certain depth of chamfering, all (final) edges of the cD have the same length; then, the hexagons are equilateral, but not regular.

The chamfer operation applied in series creates progressively larger polyhedra with new faces, hexagonal, replacing the edges of the current one. The chamfer operator transforms GP(m,n) to GP(2m,2n).

The cC is the Minkowski sum of a rhombic dodecahedron and a cube of edge length 1 when the eight order-3 vertices of the rhombic dodecahedron are at ( ± 1 , ± 1 , ± 1 ) {\displaystyle (\pm 1,\pm 1,\pm 1)} and its six order-4 vertices are at the permutations of ( ± 3 , 0 , 0 ) . {\displaystyle (\pm {\sqrt {3}},0,0).}