User:Tomruen/Andreini tessellation
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[edit] Cubic forms {4,3,4}
| name | Schläfli symbol | cell-3 {4,3} |
cell-2 | cell-1 | cell-0 {4,3} |
Solids (Partial) |
Frames (Perspective) |
vertex figure |
|---|---|---|---|---|---|---|---|---|
| cubic | t0{4,3,4} |  (4.4.4) |
 |
 |
 octahedron |
|||
| truncated cubic | t0,1{4,3,4} |  (3.8.8) |
 (3.3.3.3) |
 |
 |
 square pyramid |
||
| rectified cubic | t1{4,3,4} |  (3.4.3.4) |
(3.3.3.3) |
 |
 |
 cuboid |
||
| cantellated cubic | t0,2{4,3,4} |  (3.4.4.4) |
(4.4.4) |
(3.4.3.4) |
 |
 |
 wedge |
|
| cantitruncated cubic | t0,1,2{4,3,4} |  (4.6.8) |
(4.4.4) |
 (4.6.6) |
 |
 |
 irregular tetrahedron |
|
| runcitruncated cubic | t0,1,3{4,3,4} | (3.8.8) |
 (4.4.8) |
(4.4.4) |
(3.4.4.4) |
 |
 |
 |
| bitruncated cubic | t1,2{4,3,4} | (4.6.6) |
(4.6.6) |
 |
 |
 isosceles tetrahedron |
||
| Runcinated cubic Same as cubic |
t0,3{4,3,4} | (4.4.4) |
(4.4.4) |
(4.4.4) |
(4.4.4) |
 |
 |
octahedron |
| omnitruncated cubic | t0,1,2,3{4,3,4} | (4.6.8) |
(4.4.8) |
(4.4.8) |
(4.6.8) |
 |
 |
 irregular tetrahedron |
[edit] Alternate cubic forms
| name | cell-3 | cell-2 | cell-1 | cell-0 | Solids (Partial) |
Frames (Perspective) |
vertex figure |
|---|---|---|---|---|---|---|---|
| alternated cubic |  (3.3.3) |
(3.3.3.3) |
 |
 |
 cuboctahedron |
||
| truncated alternated cubic | (4.6.6) |
 (3.6.6) |
(3.4.3.4) |
 |
 |
 |
|
| runcinated alternated cubic | (3.4.4.4) |
(4.4.4) |
(3.3.3) |
 |
 |
 |
|
| cantitruncated alternated cubic | (4.6.8) |
(3.8.8) |
(3.6.6) |
 |
 |
 |
|
| bitruncated alternated cubic | (3.6.6) |
(3.3.3) |
(3.3.3) |
(3.6.6) |
 |
 |
 |
[edit] Elongated and gyrated
| name | cell types (# at each vertex) | # families of continuous face planes | Solids (Partial) |
Frames (Perspective) |
vertex figure |
|---|---|---|---|---|---|
| gyrated triangular prismatic |  (3.4.4) (12) |
1 square |  |
 |
|
| gyroelongated triangular prismatic | (3.4.4) (6) (4.4.4) (4) |
1 square |  |
 |
|
| gyrated alternated cubic | (3.3.3) (8) (3.3.3.3) (6) |
1 triangle |  |
 |
 |
| elongated alternated cubic | (3.4.4) (6) (3.3.3) (4) (3.3.3.3) (3) |
1 triangle |  |
 |
|
| gyroelongated alternated cubic | (3.4.4) (6) (3.3.3) (4) (3.3.3.3) (3) |
1 triangle |  |
|
