q x3o

Acronym	...
Name	q x3o, variation of triangular prism, vertex figure of rectified tesseract
Circumradius	sqrt(5/6) = 0.912871
Lace city in approx. ASCII-art	o o x x
Volume	sqrt(6)/4 = 0.612372
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Dihedral angles	between x3o and q x: 90° between q x and q x (at q): 60°
Face vector	6, 9, 5
Confer	general prisms: n-p n/d-p uniform variant: trip variations: v x3o f x3o u x3o x q3o x f3o x h3o x u3o v f3o f v3o

using edge sizes x = 1 and q = sqrt(2) = 1.414214

Incidence matrix according to Dynkin symbol

q x3o

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

xx3oo&#q   → height = sqrt(2) = 1.414214
({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&#q | 1 1 | * 3 * | 0 2 0
.x ..    | 0 2 | * * 3 | 0 1 1
---------+-----+-------+------
x.3o.    | 3 0 | 3 0 0 | 1 * *
xx ..&#q | 2 2 | 1 2 1 | * 3 *
.x3.o    | 0 3 | 0 0 3 | * * 1

qq ox&#x   → height = sqrt(3)/2 = 0.866025
(q-line || (q,x)-{4})

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

qqq&#x   → all heights = 1
(q-line || (q-line || q-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
-------+-------+-------------+--------
q..    | 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
.q.    | 0 2 0 | * * * 1 * * | 1 0 0 1
.oo&#x | 0 1 1 | * * * * 2 * | 0 0 1 1
..q    | 0 0 2 | * * * * * 1 | 0 1 0 1
-------+-------+-------------+--------
qq.&#x | 2 2 0 | 1 2 0 1 0 0 | 1 * * *
q.q&#x | 2 0 2 | 1 0 2 0 0 1 | * 1 * *
ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * * 2 *
.qq&#x | 0 2 2 | 0 0 0 1 2 1 | * * * 1

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