x h3o

Acronym	...
Name	x h3o, variation of triangular prism
Circumradius	sqrt(5)/2 = 1.118034
Lace city in approx. ASCII-art	o o h h
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Dihedral angles	between h3o and x h: 90° between x h and x h (at x): 60°
Face vector	6, 9, 5
Confer	general prisms: n-p n/d-p uniform variant: trip variations: v x3o q x3o f x3o u x3o x q3o x f3o x u3o v f3o f v3o

Incidence matrix according to Dynkin symbol

x h3o

. . . | 6 | 1 2 | 2 1
------+---+-----+----
x . . | 2 | 3 * | 2 0
. h . | 2 | * 6 | 1 1
------+---+-----+----
x h . | 4 | 2 2 | 3 *
. h3o | 3 | 0 3 | * 2

x2s6o

demi( . . . ) | 6 | 1 2 | 1 2
--------------+---+-----+----
demi( x . . ) | 2 | 3 * | 0 2
sefa( . s6o ) | 2 | * 6 | 1 1
--------------+---+-----+----
      . s6o   ♦ 3 | 0 3 | 2 *
sefa( x2s6o ) | 4 | 2 2 | * 3

starting figure: x2x6o

x2s3s

demi( . . . ) | 6 | 1 2 | 1 2
--------------+---+-----+----
demi( x . . ) | 2 | 3 * | 0 2
sefa( . s3s ) | 2 | * 6 | 1 1  h
--------------+---+-----+----
      . s3s   ♦ 3 | 0 3 | 2 *
sefa( x2s3s ) | 4 | 2 2 | * 3

starting figure: x2x3x

hh3oo&#x   → height = 1
(h-{3} || h-{3})

o.3o.    | 3 * | 2 1 0 | 1 2 0
.o3.o    | * 3 | 0 1 2 | 0 2 1
---------+-----+-------+------
h. ..    | 2 0 | 3 * * | 1 1 0
oo3oo&#x | 1 1 | * 3 * | 0 2 0
.h ..    | 0 2 | * * 3 | 0 1 1
---------+-----+-------+------
h.3o.    | 3 0 | 3 0 0 | 1 * *
hh ..&#x | 2 2 | 1 2 1 | * 3 *
.h3.o    | 0 3 | 0 0 3 | * * 1

xx oh&#h   → height = 3/2 = 1.5
(line || (x,h)-{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&#h | 1 1 | * 4 * * | 1 1 0
.x ..    | 0 2 | * * 2 * | 1 0 1
.. .h    | 0 2 | * * * 2 | 0 1 1
---------+-----+---------+------
xx ..&#h | 2 2 | 1 2 1 0 | 2 * *
.. oh&#h | 1 2 | 0 2 0 1 | * 2 *
.x .h    | 0 4 | 0 0 2 2 | * * 1

xxx&#h   → all heights = sqrt(3) = 1.732051
(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.&#h | 1 1 0 | * 2 * * * * | 1 0 1 0
o.o&#h | 1 0 1 | * * 2 * * * | 0 1 1 0
.x.    | 0 2 0 | * * * 1 * * | 1 0 0 1
.oo&#h | 0 1 1 | * * * * 2 * | 0 0 1 1
..x    | 0 0 2 | * * * * * 1 | 0 1 0 1
-------+-------+-------------+--------
xx.&#h | 2 2 0 | 1 2 0 1 0 0 | 1 * * *
x.x&#h | 2 0 2 | 1 0 2 0 0 1 | * 1 * *
ooo&#h | 1 1 1 | 0 1 1 0 1 0 | * * 2 *
.xx&#h | 0 2 2 | 0 0 0 1 2 1 | * * * 1

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