Acronym | ... |
Name |
q x3o3o, variation of tetrahedron prism, vertex figure of rectified penteract |
Circumradius | sqrt(7/8) = 0.935414 |
Volume | 1/6 = 0.166667 |
Face vector | 8, 16, 14, 6 |
Confer |
using edge sizes x = 1 and q = sqrt(2) = 1.414214
Incidence matrix according to Dynkin symbol
q x3o3o . . . . | 8 | 1 3 | 3 3 | 3 1 --------+---+------+-----+---- q . . . | 2 | 4 * | 3 0 | 3 0 . x . . | 2 | * 12 | 1 2 | 2 1 --------+---+------+-----+---- q x . . | 4 | 2 2 | 6 * | 2 0 . x3o . | 3 | 0 3 | * 8 | 1 1 --------+---+------+-----+---- q x3o . ♦ 6 | 3 6 | 3 2 | 4 * . x3o3o ♦ 4 | 0 6 | 0 4 | * 2
xx3oo3oo&#q → height = sqrt(2) = 1.414214
(tet || tet)
o.3o.3o. | 4 * | 3 1 0 | 3 3 0 | 1 3 0
.o3.o3.o | * 4 | 0 1 3 | 0 3 3 | 0 3 1
------------+-----+-------+-------+------
x. .. .. | 2 0 | 6 * * | 2 1 0 | 1 2 0
oo3oo3oo&#q | 1 1 | * 4 * | 0 3 0 | 0 3 0
.x .. .. | 0 2 | * * 6 | 0 1 2 | 0 2 1
------------+-----+-------+-------+------
x.3o. .. | 3 0 | 3 0 0 | 4 * * | 1 1 0
xx .. ..&#q | 2 2 | 1 2 1 | * 6 * | 0 2 0
.x3.o .. | 0 3 | 0 0 3 | * * 4 | 0 1 1
------------+-----+-------+-------+------
x.3o.3o. ♦ 4 0 | 6 0 0 | 4 0 0 | 1 * *
xx3oo ..&#q ♦ 3 3 | 3 3 3 | 1 3 1 | * 4 *
.x3.o3.o ♦ 0 4 | 0 0 6 | 0 0 4 | * * 1
qq ox3oo&#x → height = sqrt(2/3) = 0.816497
(line || q x3o)
o. o.3o. | 2 * | 1 3 0 0 | 3 3 0 0 | 3 1 0
.o .o3.o | * 6 | 0 1 1 2 | 1 2 2 1 | 2 1 1
------------+-----+---------+---------+------
q. .. .. | 2 0 | 1 * * * | 3 0 0 0 | 3 0 0
oo oo3oo&#x | 1 1 | * 6 * * | 1 2 0 0 | 2 1 0
.q .. .. | 0 2 | * * 3 * | 1 0 2 0 | 2 0 1
.. .x .. | 0 2 | * * * 6 | 0 1 1 1 | 1 1 1
------------+-----+---------+---------+------
qq .. ..&#x | 2 2 | 1 2 1 0 | 3 * * * | 2 0 0
.. ox ..&#x | 1 2 | 0 2 0 1 | * 6 * * | 1 1 0
.q .x .. | 0 4 | 0 0 2 2 | * * 3 * | 1 0 1
.. .x3.o | 0 3 | 0 0 0 3 | * * * 2 | 0 1 1
------------+-----+---------+---------+------
qq ox ..&#x ♦ 2 4 | 1 4 2 2 | 2 2 1 0 | 3 * *
.. ox3oo&#x ♦ 1 3 | 0 3 0 3 | 0 3 0 1 | * 2 *
.q .x3.o ♦ 0 6 | 0 0 3 6 | 0 0 3 2 | * * 1
qq xo ox&#x → height = 1/sqrt(2) = 0.707107
((q,x)-{4} || ortho (q,x)-{4})
o. o. o. | 4 * | 1 1 2 0 0 | 1 2 2 1 0 | 2 1 1
.o .o .o | * 4 | 0 0 2 1 1 | 0 2 1 2 1 | 1 2 1
------------+-----+-----------+-----------+------
q. .. .. | 2 0 | 2 * * * * | 1 2 0 0 0 | 2 1 0
.. x. .. | 2 0 | * 2 * * * | 1 0 2 0 0 | 2 0 1
oo oo oo&#x | 1 1 | * * 8 * * | 0 1 1 1 0 | 1 1 1
.q .. .. | 0 2 | * * * 2 * | 0 2 0 0 1 | 1 2 0
.. .. .x | 0 2 | * * * * 2 | 0 0 0 2 1 | 0 2 1
------------+-----+-----------+-----------+------
q. x. .. | 4 0 | 2 2 0 0 0 | 1 * * * * | 2 0 0
qq .. ..&#x | 2 2 | 1 0 2 1 0 | * 4 * * * | 1 1 0
.. xo ..&#x | 2 1 | 0 1 2 0 0 | * * 4 * * | 1 0 1
.. .. ox&#x | 1 2 | 0 0 2 0 1 | * * * 4 * | 0 1 1
.q .. .x | 0 4 | 0 0 0 2 2 | * * * * 1 | 0 2 0
------------+-----+-----------+-----------+------
qq xo ..&#x ♦ 4 2 | 2 2 4 1 0 | 1 2 2 0 0 | 2 * *
qq .. ox&#x ♦ 2 4 | 1 0 4 2 2 | 0 2 0 2 1 | * 2 *
.. xo ox&#x ♦ 2 2 | 0 1 4 0 1 | 0 0 2 2 0 | * * 2
or o. o. o. & | 8 | 1 1 1 | 1 2 3 | 3 1 --------------+---+-------+-------+---- q. .. .. & | 2 | 4 * * | 1 2 0 | 3 0 .. x. .. & | 2 | * 4 * | 1 0 2 | 2 1 oo oo oo&#x | 2 | * * 8 | 0 1 2 | 2 1 --------------+---+-------+-------+---- q. x. .. & | 4 | 2 2 0 | 2 * * | 2 0 qq .. ..&#x | 4 | 2 0 2 | * 4 * | 2 0 .. xo ..&#x & | 3 | 0 1 2 | * * 8 | 1 1 --------------+---+-------+-------+---- qq xo ..&#x & ♦ 6 | 3 2 4 | 1 2 2 | 4 * .. xo ox&#x ♦ 4 | 0 2 4 | 0 0 4 | * 2
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