In
geometry, the rectified truncated cube is a
polyhedron, constructed as a
rectified,
truncated cube. It has 38 faces: 8
equilateral triangles, 24
isosceles triangle
In geometry, an isosceles triangle () is a triangle that has two sides of equal length. Sometimes it is specified as having ''exactly'' two sides of equal length, and sometimes as having ''at least'' two sides of equal length, the latter versio ...
s, and 6
octagon
In geometry, an octagon (from the Greek ὀκτάγωνον ''oktágōnon'', "eight angles") is an eight-sided polygon or 8-gon.
A '' regular octagon'' has Schläfli symbol and can also be constructed as a quasiregular truncated square, t, whi ...
s.
Topologically, the triangles corresponding to the cube's vertices are always equilateral, although the octagons, while having equal edge lengths, do not have the same edge lengths with the equilateral triangles, having different but alternating angles, causing the other triangles to be
isosceles instead.
Related polyhedra
The ''rectified truncated cube'' can be seen in sequence of
rectification
Rectification has the following technical meanings:
Mathematics
* Rectification (geometry), truncating a polytope by marking the midpoints of all its edges, and cutting off its vertices at those points
* Rectifiable curve, in mathematics
* Recti ...
and
truncation
In mathematics and computer science, truncation is limiting the number of digits right of the decimal point.
Truncation and floor function
Truncation of positive real numbers can be done using the floor function. Given a number x \in \mathbb ...
operations from the
cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. Viewed from a corner it is a hexagon and its net is usually depicted as a cross.
The cube is the only r ...
. Further truncation, and
alternation operations creates two more polyhedra:
See also
*
Rectified truncated tetrahedron
In geometry, the rectified truncated tetrahedron is a polyhedron, constructed as a Rectification (geometry), rectified, truncated tetrahedron. It has 20 faces: 4 equilateral triangles, 12 isosceles triangles, and 4 regular hexagons.
Topologicall ...
*
Rectified truncated octahedron
In geometry, the rectified truncated octahedron is a convex polyhedron, constructed as a Rectification (geometry), rectified, truncated octahedron. It has 38 faces: 24 isosceles triangles, 6 squares, and 8 hexagons.
Topologically, the squares co ...
*
Rectified truncated dodecahedron
In geometry, the rectified truncated dodecahedron is a convex polyhedron, constructed as a rectified, truncated dodecahedron. It has 92 faces: 20 equilateral triangles, 60 isosceles triangles, and 12 decagons.
Topologically, the triangles ...
*
Rectified truncated icosahedron
In geometry, the rectified truncated icosahedron is a convex polyhedron. It has 92 faces: 60 isosceles triangles, 12 regular pentagons, and 20 regular hexagons. It is constructed as a rectification (geometry), rectified, truncated icosahedron, re ...
References
*
Coxeter ''
Regular Polytopes'', Third edition, (1973), Dover edition, (pp. 145–154 Chapter 8: Truncation)
*
John H. Conway
John Horton Conway (26 December 1937 – 11 April 2020) was an English people, English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to ...
, Heidi Burgiel, Chaim Goodman-Strauss, ''The Symmetries of Things'' 2008,
External links
George Hart's Conway interpreter generates polyhedra in
VRML, taking Conway notation as input
{{Polyhedron-stub
Polyhedra