stacked polytope is a polytope formed from a simplex by repeatedly gluing another simplex onto one of its facets. Every simplex is itself a stacked polytope...

k-dimensional stacked polytopes, polytopes formed by starting from a simplex and then repeatedly gluing simplices onto the faces of the polytope, are k-trees...

graphs, the uniquely 4-colorable planar graphs, and the graphs of stacked polytopes. They are named after Apollonius of Perga, who studied a related circle-packing...

can be stacked face-to-face in a chiral aperiodic chain called the Boerdijk–Coxeter helix. In four dimensions, all the convex regular 4-polytopes with tetrahedral...

and Stacked Polytopes", Discrete & Computational Geometry, 55 (4): 801–826, doi:10.1007/s00454-016-9777-3 Mattheo, Nicholas (2015), Convex polytopes and...

three-dimensional space. When four cubes are stacked vertically, and the other four are attached to the second-from-top cube of the stack, the resulting polycube is Dali...

In geometry, the 120-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {5,3,3}. It is also called...

In geometry, the 600-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,3,5}. It is also known...

In four-dimensional geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,4,3}...

tables Stacks and Queues Heap Graphs Trees Objects Integers Floats Variables Languages Points, Lines, Line segments, Polytopes, Regular polytopes Polygons...

July 2024 (link) Demaine, Erik D.; Schulz, André (2017), "Embedding stacked polytopes on a polynomial-size grid", Discrete & Computational Geometry, 57...

stacking of Platonic solids, the Boerdijk–Coxeter helix is not rotationally repetitive in 3-dimensional space. Even in an infinite string of stacked tetrahedra...

antiprism or pentagonal double antiprismoid is a uniform 4-polytope (4-dimensional uniform polytope) bounded by 320 cells: 20 pentagonal antiprisms, and 300...

general class of toric varieties, this information is also encoded in a polytope, which creates a powerful connection of the subject with convex geometry...

Technical drawing Weisstein, Eric W. "Polytope Edge". From Wolfram MathWorld. TeX software(TeX), Draw cube with dashed hidden lines. From TeX StackExchange....

zonohedra. 1900: Thorold Gosset enumerated the list of semiregular convex polytopes with regular cells (Platonic solids) in his publication On the Regular...

non-Euclidean spaces, such as hyperbolic honeycombs. Any finite uniform polytope can be projected to its circumsphere to form a uniform honeycomb in spherical...

hull is a convex polyhedron in three dimensions, or in general a convex polytope for any number of dimensions, whose vertices are some of the points in...

non-Euclidean spaces, such as hyperbolic uniform honeycombs. Any finite uniform polytope can be projected to its circumsphere to form a uniform honeycomb in spherical...

geometry, an infinite skew polygon or skew apeirogon is an infinite 2-polytope with vertices that are not all colinear. Infinite zig-zag skew polygons...

polyhedron. If it is bounded, then it is a convex polytope. Each BFS corresponds to a vertex of this polytope.: 53–56  As mentioned above, every basis B defines...

plane curve Concave polygon – Simple polygon which is not convex Convex polytope – Convex hull of a finite set of points in a Euclidean space Cyclic polygon –...

Komei Fukuda in 1991, for problems of generating the vertices of convex polytopes and the cells of arrangements of hyperplanes. They were formalized more...

ISBN 0-486-23729-X. rhombo-hexagonal dodecahedron, p169 H.S.M. Coxeter, Regular Polytopes, Third edition, (1973), Dover edition, ISBN 0-486-61480-8 p. 257 Weisstein...

by a unique complex tessellation of Witting polytopes, also with 240 vertices. Each complex Witting polytope is made of Hessian polyhedral cells that have...

1007/s00283-010-9138-7, hdl:1773/15593, MR 2747698 Coxeter, Harold (1973), Regular polytopes, Dover Publications Economic Mineralogy: A Practical Guide to the Study...

non-Euclidean spaces, such as hyperbolic uniform honeycombs. Any finite uniform polytope can be projected to its circumsphere to form a uniform honeycomb in spherical...

polygon (forming a Klemperer rosette), a Platonic solid, or a regular polytope in higher dimensions. The centrality of the configuration follows from...

manifold is its Euler characteristic. Leonhard Euler showed that for a convex polytope in the three-dimensional Euclidean space with V vertices (or corners),...

polygon Volume Four Spacetime Fourth spatial dimension Convex regular 4-polytope Quaternion 4-manifold Polychoron Rotations in 4-dimensional Euclidean space...