Acronym so
Name stella octangula,
compound of 2 tet
Coxeter symbol {4,3}[2{3,3}]{3,4}
 
 © ©
Circumradius sqrt(3/8) = 0.612372
Inradius 1/sqrt(24) = 0.204124
Vertex figure [33]
General of army cube
Colonel of regiment (is itself locally convex)
Dihedral angles
(at margins)
  • between {3} and {3}:   arccos(1/3) = 70.528779°
Confer
related compounds:
sis  
general polytopal classes:
regular  
External
links
hedrondude   wikipedia   mathworld

The common intersection of the stella octangula is a (scaled) oct. Moreover stella octangula is selfdual.

Aside: In projective space even a third tetrahedron could be added such, that the edges all intersect by three. In fact one vertex then would be at the center and the others at the plane of infinity. This configuration then is known as the desmic tetrahedra: a representation of a desmic configuration of 3 sets of points (here: the vertices of either tetrahedron), where any line through 2 points from 2 of these sets also passes through a point of the third set.


Incidence matrix according to Dynkin symbol

xo3oo3ox

o.3o.3o.  & | 8 |  3 | 3 || 1
------------+---+----+---++--
x. .. ..  & | 2 | 12 | 2 || 1
------------+---+----+---++--
x.3o. ..  & | 3 |  3 | 8 || 1
------------+---+----+---++--
x.3o.3o.  &  4 |  6 | 4 || 2

o3o4β

both( . . . ) | 8 |  3 | 3 || 1
--------------+---+----+---++--
both( . o4s ) | 2 | 12 | 2 || 1
--------------+---+----+---++--
sefa( o3o4β ) | 3 |  3 | 8 || 1
--------------+---+----+---++--
both( o3o4s )  4 |  6 | 4 || 2

starting figure: o3o4x

β2o4β

both( . . . ) | 8 | 2 1 | 3 || 1
--------------+---+-----+---++--
both( s 2 s ) | 2 | 8 * | 2 || 1
both( . o4s ) | 2 | * 4 | 2 || 1
--------------+---+-----+---++--
sefa( β2o4β ) | 3 | 2 1 | 8 || 1
--------------+---+-----+---++--
both( s2o4s )  4 | 4 2 | 4 || 2

starting figure: x o4x

β2β2β

both( . . . ) | 8 | 1 1 1 | 3 || 1
--------------+---+-------+---++--
both( s2s . ) | 2 | 4 * * | 2 || 1
both( s 2 s ) | 2 | * 4 * | 2 || 1
both( . s2s ) | 2 | * * 4 | 2 || 1
--------------+---+-------+---++--
sefa( β2β2β ) | 3 | 1 1 1 | 8 || 1
--------------+---+-------+---++--
both( s2s2s )  4 | 2 2 2 | 4 || 2

starting figure: x x x

© 2004-2016
top of page