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In Wenninger's book Polyhedron Models, the final stellation of the icosahedron is included as the 17th model of stellated icosahedra with index number W 42. [ 7 ] In 1995, Andrew Hume named it in his Netlib polyhedral database as the echidnahedron after the echidna or spiny anteater, a small mammal that is covered with coarse hair and spines ...
Icosahedron: Small triambic icosahedron: Icosahedron: Great triambic icosahedron: Icosahedron: Compound of five cubes: Rhombic triacontahedron: Compound of great icosahedron and great stellated dodecahedron: Icosidodecahedron: Compound of great icosahedron and great stellated dodecahedron: Great icosidodecahedron: Compound of dodecahedron and ...
As a self-dual hexadecahedron, it is one of 302404 forms, 1476 with at least order 2 symmetry, and the only one with tetrahedral symmetry. [3] As a diminished regular dodecahedron, with 4 vertices removed, the quadrilaterals faces are trapezoids. As a stellation of the regular icosahedron it is one of 32 stellations defined with tetrahedral ...
The set f 1 further subdivides into right- and left-handed forms, respectively f 1 (plain type) and f 1 (italic). Where a stellation has all cells present within an outer shell, the outer shell is capitalised and the inner omitted, for example a + b + c + e 1 is written as Ce 1 .
The polyhedra are grouped in 5 tables: Regular (1–5), Semiregular (6–18), regular star polyhedra (20–22,41), Stellations and compounds (19–66), and uniform star polyhedra (67–119). The four regular star polyhedra are listed twice because they belong to both the uniform polyhedra and stellation groupings.
In his view the great stellation is related to the icosahedron as the small one is to the dodecahedron. [ 4 ] These naïve definitions are still used. E.g. MathWorld states that the two star polyhedra can be constructed by adding pyramids to the faces of the Platonic solids.
It is a stellation of the rhombic triacontahedron, and can also be called small stellated triacontahedron. Its dual is the dodecadodecahedron. Its 24 vertices are all on the 12 axes with 5-fold symmetry (i.e. each corresponds to one of the 12 vertices of the icosahedron). This means that on each axis there is an inner and an outer vertex.
In geometry, the small triambic icosahedron is a star polyhedron composed of 20 intersecting non-regular hexagon faces. It has 60 edges and 32 vertices , and Euler characteristic of −8. It is an isohedron , meaning that all of its faces are symmetric to each other.