5-cell - Wikipedia
The 5-cell, also known as a hypertetrahedron, is the simplest possible 4-polytope with five tetrahedral cells. Learn about its properties, construction, projections, and related polytopes and honeycombs.
Rectified 5-cell - Wikipedia
A rectified 5-cell is a uniform 4-polytope composed of 5 tetrahedra and 5 octahedra. Learn about its properties, structure, symmetry, coordinates, and related polytopes.
Cantellated 5-cell - Wikipedia
In four-dimensional geometry, a cantellated 5-cell is a convex uniform 4-polytope, being a cantellation (a 2nd order truncation, up to edge-planing) of the regular 5-cell.
Pentachoron - Polytope Wiki
The pentachoron (OBSA: pen), also commonly called the 5-cell or the 4-simplex, is the simplest possible non-degenerate polychoron. The full symmetry version has 5 regular tetrahedra as cells, joining 3 to an edge and 4 to a vertex, and is one of the 6 convex regular polychora.
5-cell - Wikiversity
2024年6月29日 · The 5-cell is a 5-vertex four-dimensional object bounded by five tetrahedral cells, also known as a pentachoron, pentatope, or tetrahedral pyramid. Learn about its geometry, structure, symmetry, coordinates, and projections in this …
Pentatope -- from Wolfram MathWorld
2024年10月21日 · The pentatope is the simplest regular figure in four dimensions, also called the 5-cell or pentachoron. It has five vertices, five three-dimensional facets, and is self-dual. Learn more about its properties, graph, and projections.
5-cell — Wikipedia Republished // WIKI 2
In geometry, the 5-cell is the convex 4-polytope with Schläfli symbol {3,3,3}. It is a 5-vertex four-dimensional object bounded by five tetrahedral cells. It is also known as a C 5, pentachoron, pentatope, pentahedroid, or tetrahedral pyramid.
What is the hypervolume of a 4D tetrahedron ($5$-cell)?
The tetrahedron is $V_3$ and the 5-cell/pentachoron is $V_4$. The height can be calculated using the centroid of the previous shape and Pythagorus' Theorem giving the following recurrence relation: $${h_n}^2 = 1 - {\left({\frac{n-1}{n}}\right)}^2{h_{n-1}}^2$$ with $h_1=1$
5-cell explained
In geometry, the 5-cell is the convex 4-polytope with Schläfli symbol. It is a 5-vertex four-dimensional object bounded by five tetrahedral cells. It is also known as a C 5, pentachoron, pentatope, pentahedroid, or tetrahedral pyramid. It is the 4-simplex (Coxeter's
5-Cell -- from Wolfram MathWorld
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