Acronym trip, 3-p
TOCID symbol (3)P
Name triangular prism,
digonal cupola,
Delone cell of unit-stacked hexagonal lattice,
vertex figure of rap
|,>,O device line pyramid prism = |>|
Circumradius sqrt(7/12) = 0.763763
Vertex figure [3,42]
Snub derivation
   
Lace city
in approx. ASCII-art
o o
x x
Coordinates
  • (1/2, 1/2, -1/sqrt(12))   & all changes of sign in all but last coord
  • (1/2, 0, 1/sqrt(3))         & all changes of sign in all but last coord
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between {3} and {4}:   90°
  • between {4} and {4}:   60°
Confer
general prisms:
n-p   n/d-p  
Grünbaumian relatives:
2trip  
related Johnson solids:
gybef  
variations:
v x3o   q x3o   f x3o   u x3o   x q3o   x f3o   x u3o   v f3o   f v3o   xx2ox&#q  
blends:
2-trip-blend  
compounds:
ro   dro   kri  
general polytopal classes:
segmentohedra  
External
links
wikipedia   WikiChoron   mathworld   quickfur

Incidence matrix according to Dynkin symbol

x x3o

. . . | 6 | 1 2 | 2 1
------+---+-----+----
x . . | 2 | 3 * | 2 0
. x . | 2 | * 6 | 1 1
------+---+-----+----
x x . | 4 | 2 2 | 3 *
. x3o | 3 | 0 3 | * 2

snubbed forms: x2β3o

s3s2x

demi( . . . ) | 6 | 1 2 | 1 2
--------------+---+-----+----
demi( . . x ) | 2 | 3 * | 0 2
sefa( s3s . ) | 2 | * 6 | 1 1
--------------+---+-----+----
      s3s .    3 | 0 3 | 2 *
sefa( s3s4x ) | 4 | 2 2 | * 3

starting figure: x3x2x

β3o2x

both( . . . ) | 6 | 1 2 | 1 2
--------------+---+-----+----
both( . . x ) | 2 | 3 * | 0 2
sefa( β3o . ) | 2 | * 6 | 1 1
--------------+---+-----+----
      β3o .    3 | 0 3 | 2 *
sefa( β3o2x ) | 4 | 2 2 | * 3

starting figure: x3o x

xx3oo&#x   → height = 1
({3} || {3})

o.3o.    | 3 * | 2 1 0 | 1 2 0
.o3.o    | * 3 | 0 1 2 | 0 2 1
---------+-----+-------+------
x. ..    | 2 0 | 3 * * | 1 1 0
oo3oo&#x | 1 1 | * 3 * | 0 2 0
.x ..    | 0 2 | * * 3 | 0 1 1
---------+-----+-------+------
x.3o.    | 3 0 | 3 0 0 | 1 * *
xx ..&#x | 2 2 | 1 2 1 | * 3 *
.x3.o    | 0 3 | 0 0 3 | * * 1

xx ox&#x   → height = sqrt(3)/2 = 0.866025
(line || {4})

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

xxoo&#xr   → height(1,2) = height(3,4) = 1
              height(2,3) = height(4,1) = sqrt(3)/2 = 0.866025
(line || (line || pt) || pt)

o(..).    | 2 * * * | 1 1 1 0 0 0 | 1 1 1 0
.(o.).    | * 2 * * | 0 1 0 1 1 0 | 1 0 1 1
.(.o).    | * * 1 * | 0 0 2 0 0 1 | 0 1 2 0
.(..)o    | * * * 1 | 0 0 0 0 2 1 | 0 0 2 1
----------+---------+-------------+--------
x(..).    | 2 0 0 0 | 1 * * * * * | 1 1 0 0
o(o.).&#x | 1 1 0 0 | * 2 * * * * | 1 0 1 0
o(.o).&#x | 1 0 1 0 | * * 2 * * * | 0 1 1 0
.(x.).    | 0 2 0 0 | * * * 1 * * | 1 0 0 1
.(o.)o&#x | 0 1 0 1 | * * * * 2 * | 0 0 1 1
.(.o)o&#x | 0 0 1 1 | * * * * * 1 | 0 0 2 0
----------+---------+-------------+--------
x(x.).&#x | 2 2 0 0 | 1 2 0 1 0 0 | 1 * * *
x(.o).&#x | 2 0 1 0 | 1 0 2 0 0 0 | * 1 * *
oooo&#xr  | 1 1 1 1 | 0 1 1 0 1 1 | * * 2 *
.(x.)o&#x | 0 2 0 1 | 0 0 0 1 2 0 | * * * 1

xxx&#x   → all heights = 1
(line || (line || line))

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

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