5-Simplex
6 vertices, 15 edges, 20 faces
Dimension Selection
Rotation Controls
Projection Mode
Display Options
Animation
Camera
Simplex Properties
Dimension:
5
Vertices:
6
Edges:
15
Faces:
20
Rotation Planes:
10
Facets:
6
Volume Formula (n-simplex with edge length a):
V = (√5 / 96√3) × a⁵ ≈ 0.0147 × a⁵
What is a Simplex?
A simplex is the generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. It is the smallest possible convex set containing a given set of points.
Why 5D?
In Constraint Theory, the 5-simplex represents the minimal constraint structure in 5-dimensional space. The dodecet encoding system uses 5D geometry to efficiently encode 12-bit geometric information.
Rotation in 5D
Unlike 3D (where rotation is around an axis), rotation in 5D happens in planes. A 5D simplex has C(5,2) = 10 independent rotation planes!