a runcinated tesseract (or runcinated 16-cell) is a convex uniform 4-polytope, being a runcination (a 3rd order truncation) of the regular tesseract. There...

In geometry, a truncated tesseract is a uniform 4-polytope formed as the truncation of the regular tesseract. There are three truncations, including a...

Cantellated 24-cell, Runcinated 24-cell, Snub 24-cell Rectified 120-cell, Truncated 120-cell, Cantellated 120-cell, Runcinated 120-cell Rectified 600-cell...

identified it in 1912 as a semiregular polytope. Runcinated 5-cell (Norman Johnson) Runcinated pentachoron Runcinated 4-simplex Expanded 5-cell/4-simplex/pentachoron...

tetrahedra. It has half the vertices of a runcinated tesseract, with its construction, called a runcic tesseract. It has two uniform constructions, as a...

in 1912 as a semiregular polytope. Runcinated 24-cell (Norman W. Johnson) Runcinated icositetrachoron Runcinated polyoctahedron Small prismatotetracontoctachoron...

In four-dimensional geometry, a runcinated 120-cell (or runcinated 600-cell) is a convex uniform 4-polytope, being a runcination (a 3rd order truncation)...

Cantellated 24-cell, Runcinated 24-cell, Snub 24-cell Rectified 120-cell, Truncated 120-cell, Cantellated 120-cell, Runcinated 120-cell Rectified 600-cell...

runcination of a tesseractic honeycomb creating runcinated tesseracts, and new tesseract, rectified tesseract and cuboctahedral prism facets. The [4,3,3,4]...

In seven-dimensional geometry, a runcinated 7-orthoplex is a convex uniform 7-polytope with 3rd order truncations (runcination) of the regular 7-orthoplex...

In six-dimensional geometry, a runcinated 6-simplex is a convex uniform 6-polytope constructed as a runcination (3rd order truncations) of the regular...

be seen as 6 of 24 faces in a Petrie polygon projection plane of the tesseract. The list (sequence A006245 in the OEIS) defines the number of solutions...

In five-dimensional geometry, a runcinated 5-orthoplex is a convex uniform 5-polytope with 3rd order truncation (runcination) of the regular 5-orthoplex...

In six-dimensional geometry, a runcinated 6-cube is a convex uniform 6-polytope with 3rd order truncations (runcination) of the regular 6-cube. There are...

Cantitruncated 5-cell Runcinated 5-cell Runcitruncated 5-cell Cantellated tesseract Cantitruncated tesseract Runcinated tesseract Runcitruncated tesseract Cantellated...

In five-dimensional geometry, a runcinated 5-cube is a convex uniform 5-polytope that is a runcination (a 3rd order truncation) of the regular 5-cube....

In six-dimensional geometry, a runcinated 6-orthplex is a convex uniform 6-polytope with 3rd order truncations (runcination) of the regular 6-orthoplex...

geometry, a cantellated tesseract is a convex uniform 4-polytope, being a cantellation (a 2nd order truncation) of the regular tesseract. There are four degrees...

In seven-dimensional geometry, a runcinated 7-cube is a convex uniform 7-polytope with 3rd order truncations (runcination) of the regular 7-cube. There...

honeycomb, containing Rectified 24-cell, runcinated tesseract, cuboctahedral prism, and 3-3 duoprism cells. Runcinated hexadecachoric tetracomb/honeycomb Small...

duals of each other (such as the tesseract and 16-cell, or the 120-cell and 600-cell), then bitruncating, runcinating or omnitruncating either produces...

Runcinated enneazetton Small prismated enneazetton (Acronym: spene) (Jonathan Bowers) The Cartesian coordinates of the vertices of the runcinated 8-simplex...

polyhedral cells around each edge is represented by {p,q,r}. For example, a tesseract, {4,3,3}, has 3 cubes, {4,3}, around an edge. In general, a regular polytope...

1 rhombitrihexagonal tiling Related uniform polychora runcinated 5-cell runcinated tesseract runcinated 24-cell runcinated 120-cell runcinated hexagonal tiling honeycomb...

tesseractic cupolae and a runcinated tesseract between them. This dissection can be seen as analogous to the 4D runcinated tesseract being dissected into two...

and cantellations. Runcinated hexateron Small prismated hexateron (Acronym: spix) (Jonathan Bowers) The vertices of the runcinated 5-simplex can be most...

honeycombs with cubic cells. The cubic honeycomb has a lower symmetry as a runcinated cubic honeycomb, with two sizes of cubes. A double symmetry construction...

center of a tesseract. The 24-cells are twice as large as the tesseracts by 4-dimensional content (hypervolume), so overall there are two tesseracts for every...

(order-4) cantitruncated cubic honeycomb, tr{4,3,4}: The runcinated order-5 cubic honeycomb or runcinated order-4 dodecahedral honeycomb , has cube, dodecahedron...

and triangular prism cells, with a mirrored sphenoid vertex figure. The runcinated hexagonal tiling honeycomb, t0,3{6,3,3}, has tetrahedron, hexagonal tiling...