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Tag Archives: solid
Eight KiteRhombus Solids, Plus Five AllKite Polyhedra — the Convex Hulls of the Thirteen ArchimedeanCatalan Compounds
In a kiterhombus solid, or KRS, all faces are either kites or rhombi, and there are at least some of both of these quadrilateraltypes as faces. I have found eight such polyhedra, all of which are formed by creating the … Continue reading
Posted in Mathematics
Tagged Archimedean, Catalan, convex hull, dual, duality, geometry, kite, Mathematics, polyehdron, polyhedra, rhombi, rhombus, solid
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A Tetrahedral Exploration of the Icosahedron
Mathematicians have discovered more than one set of rules for polyhedral stellation. The software I use for rapidly manipulating polyhedra (Stella 4d, available here, including as a free trial download) lets the user choose between different sets of stellation criteria, … Continue reading
Posted in Mathematics
Tagged cuboctahedral, geometry, icosahedral, icosahedron, icosidodecahedral, Mathematics, octahedral, polyhedra, polyhedral, polyhedron, pyritohedral, solid, stellation, symmetry, tetrahedral
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Variations of the Snub Dodecahedron
To make the first of these variations, above, I augmented each triangular face of a snub dodecahedron with an antiprism 2.618 times as tall as the triangles’ edge length, and then took the convex hull of the result. The other … Continue reading
Posted in Mathematics
Tagged geometry, Mathematics, polyhedra, polyhedron, snub dodecahedron, solid, variant, variation
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Standard and Faceted Versions, Side by Side, of Each of the Thirteen Archimedean Solids
These two polyhedra are the truncated tetrahedron on the left, plus at least one faceted version of that same Archimedean solid on the right. As you can see, in each case, the figures have the same set of vertices — … Continue reading
Posted in Mathematics
Tagged Archimedean, chiral, chirality, compound, facet, faceted, faceting, geometry, Mathematics, polyhedra, polyhedral, polyhedron, solid
1 Comment
On Polyhedral Augmentation and Excavation
I have made many posts here using polyhedral augmentation, but what I haven’t done — yet — is explain it. I have also neglected the reciprocal function of augmentation, which is called excavation. It is now time to fix both … Continue reading
Posted in Mathematics
Tagged augmentation, cluster, excavation, geometry, icosahedron, icosidodecahedron, Mathematics, polyhedra, polyhedral, polyhedron, reciprocal, solid
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The Cone Problem (The Easier Sequel to the Hemisphere Problem)
That hemisphere problem (see previous two posts) was quite difficult. I’m going to unwind a bit with the much easier cone version of the same problem: at what height x above the ground, expressed as a fraction of h, must … Continue reading
Posted in Mathematics
Tagged cone, frustrum, geometry, Mathematics, problem, solid, solids, volume
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Working Towards a Solution of the Hemisphere Problem
The hemisphere problem referred to here was described in the previous post. To reword it somewhat, consider this hemisphere, half of a sphere of radius r. The orange crosssection is a circle parallel to the hemisphere’s yellow, circular base. We … Continue reading
Posted in Mathematics
Tagged geometry, graph, hemisphere, Mathematics, problem, solid, sphere
3 Comments