Acronym tridpy (alt.: trit), J12
Name trigonal dipyramid,
(line-)triangle-tegum
 
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Vertex figure [33], [34]
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between {3} and {3} (equatorial):   arccos(-7/9) = 141.057559°
  • between {3} and {3} (lacing):   arccos(1/3) = 70.528779°
Confer
uniform relative:
tet  
related Johnson solids:
etidpy  
variations:
co oo3ox&#zy (c = y = 2/3, trip dual)   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)  
general polytopal classes:
Johnson solids   deltahedra   bistratic lace towers  
External
links
wikipedia   mathworld   quickfur  

Incidence matrix according to Dynkin symbol

oxo3ooo&#xt   → both heights = sqrt(2/3) = 0.816497
(pt || pseudo {3} || pt)

o..3o..    | 1 * * | 3 0 0 | 3 0
.o.3.o.    | * 3 * | 1 2 1 | 2 2
..o3..o    | * * 1 | 0 0 3 | 0 3
-----------+-------+-------+---
oo.3oo.&#x | 1 1 0 | 3 * * | 2 0
.x.3...    | 0 2 0 | * 3 * | 1 1
.oo3.oo&#x | 0 1 1 | * * 3 | 0 2
-----------+-------+-------+----
ox.3...&#x | 1 2 0 | 2 1 0 | 3 *
.xo3...&#x | 0 2 1 | 0 1 2 | * 3
or
o..3o..     & | 2 * | 3 0 | 3
.o.3.o.       | * 3 | 2 2 | 4
--------------+-----+-----+--
oo.3oo.&#x  & | 1 1 | 6 * | 2
.x.3...       | 0 2 | * 3 | 2
--------------+-----+-----+--
ox.3...&#x  & | 1 2 | 2 1 | 6

yo ox3oo&#zx   → height = 0   (y = sqrt(8/3) = 1.632993)
(tegum product of line with {3})

o. o.3o.    | 2 * | 3 0 | 3
.o .o3.o    | * 3 | 2 2 | 4
------------+-----+-----+--
oo oo3oo&#x | 1 1 | 6 * | 2
.. .x3.o    | 0 2 | * 3 | 2
------------+-----+-----+--
.. ox ..&#x | 1 2 | 2 1 | 6

oyo oox&#xt   → height(1,2) = 1/sqrt(3) = 0.577350
                height(2,3) = 1/sqrt(12) = 0.288675
                y = sqrt(8/3) = 1.632993
(pt || pseudo y-line || perp line)

o.. o..    | 1 * * | 2 2 0 0 | 4 0
.o. .o.    | * 2 * | 1 0 2 0 | 2 1
..o ..o    | * * 2 | 0 1 2 1 | 2 2
-----------+-------+---------+----
oo. oo.&#x | 1 1 0 | 2 * * * | 2 0
o.o o.o&#x | 1 0 1 | * 2 * * | 2 0
.oo .oo&#x | 0 1 1 | * * 4 * | 1 1
... ..x    | 0 0 2 | * * * 1 | 0 2
-----------+-------+---------+----
ooo ooo&#x | 1 1 1 | 1 1 1 0 | 4 *
... .ox&#x | 0 1 2 | 0 0 2 1 | * 2

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