User:Tomruen/Andreini tessellation

From Wikipedia, the free encyclopedia

[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