In Conway polyhedron notation, it can represented as "'pT "', applying George W . Hart's propeller operator to a regular tetrahedron.
22.
The symmetries of a regular tetrahedron correspond to those of a cube which map each tetrahedron to itself; the other symmetries of the cube map the two to each other.
23.
The three spheres are all already touching each other, forming an equilateral triangle, and since they all touch the new sphere, the four centers form a regular tetrahedron.
24.
However, Herschel's paper described solutions for the Icosian game only on the graphs of the regular tetrahedron and regular icosahedron; it did not describe the Herschel graph.
25.
The "'trigonal "'or "'triangular pyramid "'with all equilateral triangles faces becomes the regular tetrahedron, one of the Platonic solids.
26.
The Reuleaux tetrahedron has the same face structure as a regular tetrahedron, but with curved faces : four vertices, and four curved faces, connected by six circular-arc edges.
27.
The paracompact complete graph diagram or, is represented as [ 3 [ 3, 3 ] ] with the superscript [ 3, 3 ] as the symmetry of its regular tetrahedron coxeter diagram.
28.
The "'Reuleaux tetrahedron "'is the intersection of four spheres of radius " s " centered at the vertices of a regular tetrahedron with side length " s ".
29.
They have been named with a " demi-" prefix to each hypercube name : demicube, demitesseract, etc . The demicube is identical to the regular tetrahedron, and the demitesseract is identical to the regular 16-cell.
30.
In the case of a regular tetrahedron, it's reasonable to assume that the 4th dimensional analog is also a regular figure-so you get the tetrahedron that shrinks to a dot as the 4 dimensional shape translated through 3-space.
