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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 Truncated tetrahedron - Polytope Wiki
See more on polytope.miraheze.orgA truncated tetrahedron of edge length 1 has vertex coordinates given by all permutations and even sign changes of: 1. ( 3 2 4 , 2 4 , 2 4 ) {\displaystyle {\displaystyle \left({\frac {3{\sqrt {2}}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}}\right)}} . Scaling these coordinates by a factor of 2 2 {\displaystyle {\displa…Article 45: Geometry - Platonic Solids - Part 6 - The …
When a tetrahedron is uniformly truncated, it forms the truncated tetrahedron, an Archimedean solid. This means all 4 vertices of a tetrahedron are truncated at one third of the original edge length.
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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), …
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” …
Truncated Tetrahedron - Geometry Calculator
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 choose the number of decimal places.
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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 …
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.
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.
Article 43: Geometry - Platonic Solids
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 …
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 …
Dense packings of the Platonic and Archimedean solids - Nature
Aug 13, 2009 · We note that the tetrahedron (P1) and truncated tetrahedron (A1) are the only Platonic and Archimedean solids, respectively, that are not centrally symmetric. A particle is …
Truncated Tetrahedron - Polyhedron Garden
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 …
Example of Platonic and Archimedean solids circumscribed by a …
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 …
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 …
(PDF) Mathematical Analysis of Truncated Tetrahedron …
All the important parameters of a truncated tetrahedron such as normal distances & solid angles subtended by the faces, inner radius, outer radius, mean radius, surface area & volume have …
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 = …
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 …
Continuous flattening of truncated tetrahedra
May 27, 2015 · In this paper, we show that a truncated regular tetrahedron can be folded continuously via explicit continuous folding mappings into a flat (folded) state, such that two of …
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