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Truncated tetrahedron - Wikipedia
In geometry, the truncated tetrahedron is an Archimedean solid. It has 4 regular hexagonal faces, 4 equilateral triangle faces, 12 vertices and 18 edges (of two types). It can be constructed by truncating all 4 vertices of a regular tetrahedron. See more
The truncated tetrahedron can be constructed from a regular tetrahedron by cutting all of its vertices off, a process known as See more
Given the edge length $${\displaystyle a}$$. The surface area of a truncated tetrahedron $${\displaystyle A}$$ is the sum of 4 regular hexagons and 4 equilateral triangles' … See more
In the mathematical field of graph theory, a truncated tetrahedral graph is an Archimedean graph, the graph of vertices and edges of … See more
The truncated tetrahedron can be found in the construction of polyhedrons. For example, the augmented truncated tetrahedron is a Johnson solid constructed from a truncated … See more
• Quarter cubic honeycomb – Fills space using truncated tetrahedra and smaller tetrahedra
• Truncated 5-cell – Similar uniform polytope in 4-dimensions
• Truncated triakis tetrahedron See moreWikipedia text under CC-BY-SA license Article 45: Geometry - Platonic Solids - Part 6 - The Tetrahedron
Truncated tetrahedron - Polytope Wiki
The truncated tetrahedron, or tut, is one of the 13 Archimedean solids, and the only one with tetrahedral symmetry. It consists of 4 triangles and 4 hexagons. Each vertex joins one triangle …
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Article 43: Geometry - Platonic Solids - Part 4
The vertices of the octahedron (shown in red) are truncated to form the truncated octahedron (shown below in green). This is the only Archimedean solid that can fill space with identical copies of itself leaving no gaps.
Dense packings of polyhedra: Platonic and Archimedean solids
Oct 5, 2009 · The truncated tetrahedron is the only non-centrally symmetric Archimedean solid, the densest known packing of which is a non-lattice packing with density at least as high as …
- Author: Salvatore Torquato, Y. Jiao
- Estimated Reading Time: 6 mins
- Publish Year: 2009
One can get 5 of them from the platonic solids by truncation. They are called ”truncated Tetra-hedron” (tI), ”truncated Cube” (tC), ”truncated Octahedron” (tO), ”truncated Dodecahedron” …
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Truncated Tetrahedron -- from Wolfram MathWorld
Mar 5, 2025 · The truncated tetrahedron is the Archimedean solid with faces 4{3}+4{6}. It is also the uniform polyhedron with Maeder index 2 (Maeder 1997), Wenninger index 6 (Wenninger 1989), Coxeter index 16 (Coxeter et al. 1954), …
Sphere-Truncated Tetrahedron by Books
Oct 2, 2024 · A tetrahedron truncated by a sphere. The author marked this model as their own original creation. | Sharing without ATTRIBUTION. | Remix Culture allowed. | Commercial Use. | Free Cultural Works. | Meets Open Definition.
The Tetrahedron and the Truncated Tetrahedron
This process shortens the side lengths of the edges in the original tetrahedron by the same amount. Notice that it also doubles the number of edges -- changing the green triangular faces of the tetrahedron (left) into green hexagonal faces in …
Paper Truncated Tetrahedron - Polyhedra
The truncated tetrahedron is one of the 13 Archimedean solids. The model is made of 4 triangels and 4 hexagons. Print the PDF file to make the paper model. The large version of the truncated tetrahedron has a circumscribed sphere …
Example of Platonic and Archimedean solids …
Example of Platonic and Archimedean solids circumscribed by a sphere. The image shows two intersecting tetrahedra that are duals to each other, one coloured in purple and the other in orange. The...
Truncated Tetrahedron, n=12. Polyhedra with extreme
The coordinates of the polyhedron are taken from the applet: Polyhedra whose vertices are equivalent and have an extreme distribution on the same sphere. The first applet sorts and …
Truncated Tetrahedron Calculator - Free Online Calc
Explore Truncated Tetrahedron calculations and utilize our efficient Truncated Tetrahedron Calculator for accurate geometric results in architecture, engineering, and design.
The truncated tetrahedron is the only non-centrally symmetric Archimedean solid, the densest known packing of which is a non-lattice packing with density at least as high as 23/24 = …
We outline the classification, up to isometry, of all tetrahedra in hyperbolic space with one or more vertices truncated, for which the dihedral angles along the edges formed by the truncations are …
Truncated Tetrahedron - Geometry Calculator - Rechneronline
A truncated tetrahedron is constructed by cutting off the vertices of a tetrahedron in a way, so that every edge has the same length. Its dual body is the triakis tetrahedron . Enter one value and …
Communication: A packing of truncated tetrahedra that nearly fills …
Oct 17, 2011 · Both the truncated-tetrahedron dimer (i.e., the truncated regular rhombohedron) and the CT packing possess 3-fold rotational symmetry, with the symmetry axes being the …
Crystalline Assemblies and Densest Packings of a Family of …
Nov 19, 2011 · Here, we study thermodynamic self-assembly of a family of truncated tetrahedra and report several atomic crystal isostructures, including diamond, β-tin, and high-pressure …
The Truncated Tetrahedron - qfbox.info
Jan 6, 2023 · The truncated tetrahedron is a 3D uniform polyhedron bounded by 8 polygons (4 hexagons and 4 triangles), 18 edges, and 12 vertices. It is the simplest of the Archimedean …
Truncated octahedron - Wikipedia
A truncated octahedron is constructed from a regular octahedron by cutting off all vertices. This resulting polyhedron has six squares and eight hexagons, leaving out six square …
Truncated Tetrahedron - NRICH
A regular tetrahedron with edges of length 6 cm has each corner cut off to produce the solid shown. The triangular faces are all equilateral triangles, but not necessarily the same size. …
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