bitruncated tetrahedral-octahedral honeycomb,
bitruncated alternated-cubic honeycomb,
quarter cubic honeycomb
©
⭳©
©
- ambification:
- recytatoh
- more general:
- xPo3o...o3oPxQ*a
links
| Acronym | cytatoh (old: batatoh) |
| Name | cyclotruncated tetrahedral-octahedral honeycomb (butnot thehyperbolic cyclotruncated octahedral-tetrahedral honeycombcytoth), bitruncated tetrahedral-octahedral honeycomb, bitruncated alternated-cubic honeycomb, quarter cubic honeycomb |
| |
| VRML |
|
| Vertex figure |
|
| Confer |
|
| External links | |
This honeycomb also can be described ass4o3o4s', i.e. as sequential applications ofalternated facetings, according tox4o3o4x →s4o3o4x (= x3o3o *b4x) → x3o3o *b4s' (cf. below).
By virtue of an outer symmetry this is a non-quasiregular monotoxal honeycomb, that is all edges belong to the same equivalence class.
Dissecting thetets into their facial centri-pyramids and re-adjoining those bits to the neighbouringtuts each, produces the right shown monotopaltriakis truncated tetrahedron honeycomb, which in turn is nothing but theVoronoi complex of theDiamond "lattice".
Incidence matrix according toDynkin symbol
x3x3o3o3*a (N → ∞). . . . | 4N♦ 3 3 | 6 3 3 | 3 3 1 1-----------+----+-------+----------+--------x . . . | 2 | 6N * | 2 2 0 | 1 2 1 0. x . . | 2 | * 6N | 2 0 2 | 2 1 0 1-----------+----+-------+----------+--------x3x . . | 6 | 3 3 | 4N * * | 1 1 0 0x . . o3*a | 3 | 3 0 | * 4N * | 0 1 1 0. x3o . | 3 | 0 3 | * * 4N | 1 0 0 1-----------+----+-------+----------+--------x3x3o .♦ 12 | 6 12 | 4 0 4 | N * * *x3x . o3*a♦ 12 | 12 6 | 4 4 0 | * N * *x . o3o3*a♦ 4 | 6 0 | 0 4 0 | * * N *. x3o3o♦ 4 | 0 6 | 0 0 4 | * * * N
or. . . . | 2N♦ 6 | 6 6 | 6 2--------------+----+----+-------+----x . . . & | 2 | 6N | 2 2 | 3 1--------------+----+----+-------+----x3x . . | 6 | 6 | 2N * | 2 0x . . o3*a & | 3 | 3 | * 4N | 1 1--------------+----+----+-------+----x3x3o . &♦ 12 | 18 | 4 4 | N *x . o3o3*a &♦ 4 | 6 | 0 4 | * N
x3x3o3/2o3/2*a (N → ∞). . . . | 4N♦ 3 3 | 6 3 3 | 3 3 1 1---------------+----+-------+----------+--------x . . . | 2 | 6N * | 2 2 0 | 1 2 1 0. x . . | 2 | * 6N | 2 0 2 | 2 1 0 1---------------+----+-------+----------+--------x3x . . | 6 | 3 3 | 4N * * | 1 1 0 0x . . o3/2*a | 3 | 3 0 | * 4N * | 0 1 1 0. x3o . | 3 | 0 3 | * * 4N | 1 0 0 1---------------+----+-------+----------+--------x3x3o .♦ 12 | 6 12 | 4 0 4 | N * * *x3x . o3/2*a♦ 12 | 12 6 | 4 4 0 | * N * *x . o3/2o3/2*a♦ 4 | 6 0 | 0 4 0 | * * N *. x3o3/2o♦ 4 | 0 6 | 0 0 4 | * * * N
x3o3o *b4s (N → ∞)demi( . . . . ) | 4N♦ 3 3 | 3 6 3 | 1 3 1 3-------------------+----+-------+----------+--------demi( x . . . ) | 2 | 6N * | 2 2 0 | 1 2 0 1 . o . *b4s | 2 | * 6N | 0 2 2 | 0 1 1 2-------------------+----+-------+----------+--------demi( x3o . . ) | 3 | 3 0 | 4N * * | 1 1 0 0sefa( x3o . *b4s ) | 6 | 3 3 | * 4N * | 0 1 0 1sefa( . o3o *b4s ) | 3 | 0 3 | * * 4N | 0 0 1 1-------------------+----+-------+----------+--------demi( x3o3o . )♦ 4 | 6 0 | 4 0 0 |N * * * x3o . *b4s♦ 12 | 12 6 | 4 4 0 | * N * * . o3o *b4s♦ 4 | 0 6 | 0 0 4 | * * N *sefa( x3o3o *b4s )♦ 12 | 6 12 | 0 4 4 | * * * Nstarting figure:x3o3o *b4x
© 2004-2025 | top of page |
