In geometry, the triakis icosahedron is an Archimedean dual solid, or a Catalan solid, with 60 isosceles triangle faces. Its dual is the truncated dodecahedron. It has also been called the kisicosahedron.[1] It was first depicted, in a non-convex form with equilateral triangle faces, by Leonardo da Vinci in Luca Pacioli's Divina proportione, where it was named the icosahedron elevatum.[2] The capsid of the Hepatitis A virus has the shape of a triakis icosahedron.[3]
^Conway, John H.; Burgiel, Heidi; Goodman-Strauss, Chaim (2008). The Symmetries of Things. AK Peters. p. 284. ISBN 978-1-56881-220-5.
^Brigaglia, Aldo; Palladino, Nicla; Vaccaro, Maria Alessandra (2018). "Historical notes on star geometry in mathematics, art and nature". In Emmer, Michele; Abate, Marco (eds.). Imagine Math 6: Between Culture and Mathematics. Springer International Publishing. pp. 197–211. doi:10.1007/978-3-319-93949-0_17.
^Zhu, Ling; Zhang, Xiaoxue (October 2014). "Hepatitis A virus exhibits a structure unique among picornaviruses". Protein & Cell. 6 (2): 79–80. doi:10.1007/s13238-014-0103-7. PMC 4312766.
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the Kleetope; the triakisicosahedron is the Kleetope of the icosahedron. This interpretation is also expressed in the name, triakis, which is used for...
The truncated triakisicosahedron, or more precisely an order-10 truncated triakisicosahedron, is a convex polyhedron with 72 faces: 10 sets of 3 pentagons...
In geometry, the great triakisicosahedron is a nonconvex isohedral polyhedron. It is the dual of the uniform great stellated truncated dodecahedron....
faces are broken into triangles, it is topologically related to the triakisicosahedron, with the same face connectivity, but much taller isosceles triangle...
vertices), or triakis tetrahedron. Building a pyramid on each face of a regular octahedron, using twelve Sonobe units, results in a triakis octahedron....
no 18-faced strictly convex deltahedron. However, the edge-contracted icosahedron gives an example of an octadecahedron that can either be made strictly...
In geometry, the truncated triakis tetrahedron, or more precisely an order-6 truncated triakis tetrahedron, is a convex polyhedron with 16 faces: 4 sets...
the visible surface is considered, it has the same topology as a triakisicosahedron with concave pyramids rather than convex ones. The excavated dodecahedron...
the triakisicosahedron, formed by adding a triangular pyramid to each face of an icosahedron. The dual polyhedron of the small triambic icosahedron is...
forms. The only Catalan solid with genuine tetrahedral symmetry is the triakis tetrahedron (dual of the truncated tetrahedron). The rhombic dodecahedron...
zodiac signs, and the third represents the 12 houses. A specialized icosahedron die provides the answers of the Magic 8 Ball, conventionally used to...
dodecahedron, an icosidodecahedron, or a truncated icosahedron and their respective duals a triakisicosahedron, a rhombic triacontahedron, or a pentakis dodecahedron...
The triakis tetrahedron is the Kleetope of a tetrahedron, the triakis octahedron is the Kleetope of an octahedron, and the triakisicosahedron is the...
be noble. Not all isozonohedra are isohedral. For example, a rhombic icosahedron is an isozonohedron but not an isohedron. A polyhedron (or polytope in...
polyhedra: It is part of a truncation process between a dodecahedron and icosahedron: This polyhedron is topologically related as a part of sequence of uniform...
Wenninger's 34th model as his 9th stellation of the icosahedronTriakisicosahedron Small triambic icosahedron Medial rhombic triacontahedron The Regular Polyhedra...
represented by its Schläfli symbol {5, 3}. The dual polyhedron is the regular icosahedron {3, 5}, having five equilateral triangles around each vertex. The convex...
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