There is only one type of edge, so truncating all the vertices to will produce an Archimedean solid.
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The edges can be contracted to points with no loss of symmetry.
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The edges can be contracted to points with no loss of symmetry.
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The edges can be contracted to points with no loss of symmetry.
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Each vertex belongs to 3 identical faces, so triangles can be added between the existing faces to produce a snub polyhedron.
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This is a snub polyhedron, so triangles can be removed to produce a simpler Platonic solid.
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Why can't I truncate the vertices?
There are multiple types of edge, so truncating would result in multiple types of vertex. The result wouldn't be Archimedean.
Why can't I contract all the edges?
Every vertex can reach every other vertex by a path of just edges, so contracting them would reduce the polyhedron to a single point.
Why can't I contract all the edges?
Every vertex can reach every other vertex by a path of just edges, so contracting them would reduce the polyhedron to a single point.
Why can't I construct a snub form?
There are multiple types of face, so a snub form would have more than one kind of vertex. The result wouldn't be Archimedean.
Special note about the octahedron:
The octahedron can be produced by contracting edges of a truncated tetrahedron, but there's no symmetry-preserving way to reverse that operation.
-> truncated tetrahedron