All Topics  
Truncated tetrahedron

 

 
   Email Print
   Bookmark   Link
 

 

Truncated tetrahedron
 
 
  Topics Truncated tetrahedron Topic Home

The truncated tetrahedron is an Archimedean solid
Archimedean solid

In geometry an Archimedean solid is a highly symmetric, semi-regular convex set polyhedron composed of two or more types of regular polygons meeting in identical vertex ....
. It has 4 regular hexagon
Hexagon

In geometry, a hexagon is a polygon with six edges and six Vertex . A regular hexagon has Schl?fli symbol ....
al faces, 4 regular triangular faces, 12 vertices and 18 edges.

area A and the volume
Volume

The volume of any solid, liquid, plasma, vacuum or theoretical object is how much three-dimensional space it occupies, often quantified numerically....
 V of a truncated tetrahedron of edge length a are:

esian coordinates for the 12 vertices of a truncated
Truncation (geometry)

In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new Facet in place of each vertex....
 tetrahedron
Tetrahedron

A tetrahedron is a polyhedron composed of four triangle faces, three of which meet at each vertex . A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids....
 centered at the origin, with edge length √8, are all permutations of (±1,±1,±3) with an even number of minus signs:

Use in architecture
Giant truncated tetrahedrons were used for the "Man the Explorer" and "Man the Producer" theme pavilions in Expo 67
Expo 67

The 1967 International and Universal Exposition, or Expo 67 as it was commonly known, was the World's Fair held in Montreal, Canada from April 27 to October 29, 1967....
.






Discussion
Ask a question about 'Truncated tetrahedron'
Start a new discussion about 'Truncated tetrahedron'
Answer questions from other users
Full Discussion Forum



Encyclopedia


The truncated tetrahedron is an Archimedean solid
Archimedean solid

In geometry an Archimedean solid is a highly symmetric, semi-regular convex set polyhedron composed of two or more types of regular polygons meeting in identical vertex ....
. It has 4 regular hexagon
Hexagon

In geometry, a hexagon is a polygon with six edges and six Vertex . A regular hexagon has Schl?fli symbol ....
al faces, 4 regular triangular faces, 12 vertices and 18 edges.

Area and volume

The area A and the volume
Volume

The volume of any solid, liquid, plasma, vacuum or theoretical object is how much three-dimensional space it occupies, often quantified numerically....
 V of a truncated tetrahedron of edge length a are:

Cartesian coordinates

Cartesian coordinates for the 12 vertices of a truncated
Truncation (geometry)

In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new Facet in place of each vertex....
 tetrahedron
Tetrahedron

A tetrahedron is a polyhedron composed of four triangle faces, three of which meet at each vertex . A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids....
 centered at the origin, with edge length √8, are all permutations of (±1,±1,±3) with an even number of minus signs:
  • (+3,+1,+1), (+1,+3,+1), (+1,+1,+3)
  • (−3,−1,+1), (−1,−3,+1), (−1,−1,+3)
  • (−3,+1,−1), (−1,+3,−1), (−1,+1,−3)
  • (+3,−1,−1), (+1,−3,−1), (+1,−1,−3)


Use in architecture


Giant truncated tetrahedrons were used for the "Man the Explorer" and "Man the Producer" theme pavilions in Expo 67
Expo 67

The 1967 International and Universal Exposition, or Expo 67 as it was commonly known, was the World's Fair held in Montreal, Canada from April 27 to October 29, 1967....
. They were made of massive girders of steel bolted together in a geometric lattice. The tetrahedrons were interconnected with lattice steel platforms. All of these buildings were demolished after the end of Expo 67, as they had not been built to withstand the severity of the Montreal weather over the years. Their only remnants are in the Montreal city archives, the Public Archives Of Canada and the photo collections of tourists of the times.

See also

  • octahedron
    Octahedron

    An octahedron is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each wikt:vertex....
  • tetrahedron
    Tetrahedron

    A tetrahedron is a polyhedron composed of four triangle faces, three of which meet at each vertex . A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids....


External links

  • The Encyclopedia of Polyhedra