- four-dimensional
Euclidean geometry, the 4-simplex honeycomb, 5-cell
honeycomb or
pentachoric-dispentachoric
honeycomb is a space-filling
tessellation honeycomb. It...
-
Direct subgroups of the
reflective 4-dimensional
point groups are:
Pentachoric group – A4, [3,3,3], (),
order 120, (Du Val #51' (I†/C1;I/C1)†*, Conway...
- {\displaystyle P_{4}(n)={\frac {n(n+1)(n+2)(n+3)}{24}}={\binom {n+3}{4}}} (
pentachoric numbers,
pentatopic numbers, 4-simplex numbers), ⋮ {\displaystyle \qquad...
- {p}×{q} - A
Cartesian product of two polygons. The 5-cell has
diploid pentachoric [3,3,3] symmetry, of
order 120,
isomorphic to the
permutations of five...
- times", πενταπλάσιος (pentaplásios) "five-fold", πενταχοῦ diapente,
pentachoric, pentad, pentagon, pentagram, pentalpha, pentapolis, pentatonic, pentatope...
- 5-cell, and
omnitruncated 5-cell (the
latter with 240 edges) all
share pentachoric symmetry [ 5 , 3 , 2 ] {\displaystyle [5,3,2]} , of
order 240; four-dimensional...
- times", πενταπλάσιος (pentaplásios) "five-fold", πενταχοῦ diapente,
pentachoric, pentad, pentagon, pentagram, pentalpha, pentapolis, pentatonic, pentatope...
-
Graph type
Linear Tridental Coxeter group and
diagram Pentachoric [3,3,3]
Hexadecachoric [4,3,3]
Icositetrachoric [3,4,3]
Hexacosichoric [5,3,3] Demitesseractic...
- has only one such construction. The
omnitruncated 5-cell has
extended pentachoric symmetry, [[3,3,3]],
order 240. The
vertex figure of the omnitruncated...
-
composed of 48
truncated cubes. This 4-polytope has a
higher extended pentachoric symmetry (2×A4, [[3,3,3]]),
doubled to
order 240,
because the element...
