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Tag Archives: chiral
A Chiral Polyhedron Made of Kites and Triangles, Along with Its Dual, Made of Triangles and Isosceles Trapezoids
To make this polyhedron using Stella 4d (available here), one starts with the icosahedron, drops the symmetry of the model down from icosahedral to tetrahedral, and then stellates it once. The result is a chiral solid featuring four triangular faces … Continue reading
Posted in Mathematics
Tagged chiral, geometry, isosceles, kite, Mathematics, polyhedra, polyhedron, trapezoid
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The 43rd Stellation of the Snub Dodecahedron, and Related Polyhedra, Part One
If you stellate the snub dodecahedron 43 times, this is the result. The yellow faces are kites, not rhombi. Like the snub dodecahedron itself, this polyhedron is chiral. Here is the mirrorimage of the polyhedron shown above. Any chiral polyhedron … Continue reading
Posted in Mathematics
Tagged chiral, compound, dual, geometry, Mathematics, polyhedra, polyhedron, stellate, stellation
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A Chiral Polyhedron with Tetrahedral Symmetry
The yellow faces of this polyhedron are parallelograms, while the red ones are trapezoids. To demonstrate its chirality, here is the compound of it, and its own mirrorimage. Both of these “virtual polyhedra” were made using Stella 4d: Polyhedron Navigator, … Continue reading
Posted in Mathematics
Tagged chiral, chirality, compound, geometry, Mathematics, polyhedra, polyhedron
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A Second ColoringScheme for the Chiral Tetrated Dodecahedron
For detailed information on this newlydiscovered polyhedron, which is near (or possibly in) the “fuzzy” borderzone between the “nearmisses” (irregularities real, but not visually apparent) and “nearnearmisses” (irregularities barely visible, but there they are) to the Johnson solids, please see … Continue reading
The Chiral Tetrated Dodecahedron: A New NearMiss?
The images above show a new nearmiss (to the Johnson solids) candidate I just found using Stella 4d, software you can try here. Like the original tetrated dodecahedron (a recognized nearmiss shown at left, below), making this polyhedron relies on … Continue reading
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
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Eight Chiral Polyhedra with Icosidodecahedral Symmetry
To see a larger version of any rotating model, simply click on it. Each of these polyhedral images was created using a program called Stella 4d, which is available here.
Posted in Mathematics
Tagged chiral, geometry, icosahedral, icosidodecahedral, Mathematics, polyhedra, polyhedron, symmetry
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