Acronym ...
Name dual of uniform triangular prism,
triangular dipyramid (but not tridpy),
o3m3o3o cell
 
 ©
Inradius 1/sqrt(21) = 0.218218
Vertex figure [T3], [t4]
Dihedral angles
  • at long edge:   arccos(-1/7) = 98.213211°
  • at short edge:   arccos(-1/7) = 98.213211°
Dual trip
Confer
more general:
m mNo  
related Johnson solids:
tridpy  
variations:
co oo3ox&#zy (c = sqrt(8)/3, y = sqrt(5)/3, ico derived)   co oo3ox&#zy (c = sqrt(2)/3, y = sqrt(7/18), tes derived)   co oo3ox&#zy (c = (sqrt(5)-1)/3, y = sqrt[(9-sqrt(5))/18, hi derived)  
External
links
wikipedia   mathworld  

The triangles {(t,t,T)} have vertex angles t = arccos[(1+5 sqrt(5))/16] = 40.423604° resp. T = arccos(-1/8) = 97.180756°.

Note that the term dipyramid, even so stated above, in general says nothing about the relative ratio of the to be chosen lacing edge size. There is an equilateral dipyramid as well, tridpy (n=3). – Whereas in here the edge ratio is chosen such as to match its duality to the trip!

The a edge, provided in the below description, only qualifies as pseudo edge wrt. the full polyhedron. In fact it rather describes its tip-to-tip distance.


Incidence matrix according to Dynkin symbol

m m3o =
oxo3ooo&#yt   → both heights = a/2 = 1/3
                y = 2/3
(pt || pseudo {3} || pt)

o..3o..    | 1 * * | 3 0 0 | 3 0  [T3]
.o.3.o.    | * 3 * | 1 2 1 | 2 2  [t4]
..o3..o    | * * 1 | 0 0 3 | 0 3  [T3]
-----------+-------+-------+----
oo.3oo.&#y | 1 1 0 | 3 * * | 2 0  y
.x. ...    | 0 2 0 | * 3 * | 1 1  x
.oo3.oo&#y | 0 1 1 | * * 3 | 0 2  y
-----------+-------+-------+----
ox. ...&#y | 1 2 0 | 2 1 0 | 3 *  {(t,t,T)}
.xo ...&#y | 0 2 1 | 0 1 2 | * 3  {(t,t,T)}

m m3o =
ao ox3oo&#zy   → height = 0
                 a = y = 2/3
(tegum product of a-line with {3})

o. o.3o.    | 2 * | 3 0 | 3  [T3]
.o .o3.o    | * 3 | 2 2 | 4  [t4]
------------+-----+-----+--
oo oo3oo&#y | 1 1 | 6 * | 2  y
.. .x ..    | 0 2 | * 3 | 2  x
------------+-----+-----+--
.. ox ..&#y | 1 2 | 2 1 | 6  {(t,t,T)}

© 2004-2019
top of page