Acronym | trippy, K-4.7 |
Name |
trigonal-prismatic pyramid, vertex pyramid of the rectified pentachoron |
|,>,O device | line pyramid prism pyramid = |>|> |
Segmentochoron display | |
Circumradius | sqrt(3/5) = 0.774597 |
Lace city in approx. ASCII-art |
o3o x3o x3o |
x o o o x x | |
Volume | sqrt(5)/32 = 0.069877 |
Dihedral angles | |
Face vector | 7, 15, 14, 6 |
Confer |
|
External links |
Incidence matrix according to Dynkin symbol
ox ox3oo&#x → height = sqrt(5/12) = 0.645497
(pt || trip)
o. o.3o. | 1 * ♦ 6 0 0 | 3 6 0 0 | 3 2 0
.o .o3.o | * 6 | 1 1 2 | 1 2 2 1 | 2 1 1
------------+-----+-------+---------+------
oo oo3oo&#x | 1 1 | 6 * * | 1 2 0 0 | 2 1 0
.x .. .. | 0 2 | * 3 * | 1 0 2 0 | 2 0 1
.. .x .. | 0 2 | * * 6 | 0 1 1 1 | 1 1 1
------------+-----+-------+---------+------
ox .. ..&#x | 1 2 | 2 1 0 | 3 * * * | 2 0 0
.. ox ..&#x | 1 2 | 2 0 1 | * 6 * * | 1 1 0
.x .x .. | 0 4 | 0 2 2 | * * 3 * | 1 0 1
.. .x3.o | 0 3 | 0 0 3 | * * * 2 | 0 1 1
------------+-----+-------+---------+------
ox ox ..&#x ♦ 1 4 | 4 2 2 | 2 2 1 0 | 3 * *
.. ox3oo&#x ♦ 1 3 | 3 0 3 | 0 3 0 1 | * 2 *
.x .x3.o ♦ 0 6 | 0 3 6 | 0 0 3 2 | * * 1
xox3ooo&#x → height(1,2) = height(2,3) = sqrt(2/3) = 0.816497
height(1,3) = 1
height(1,23) = sqrt(5/8) = 0.790569
shear(1,23) = 1/sqrt(6) = 0.408248
({3} || tet)
o..3o.. | 3 * * | 2 1 1 0 0 | 1 2 2 1 0 0 | 1 1 2 0
.o.3.o. | * 1 * ♦ 0 3 0 3 0 | 0 3 0 3 3 0 | 1 0 3 1
..o3..o | * * 3 | 0 0 1 1 2 | 0 0 2 1 2 1 | 0 1 2 1
-----------+-------+-----------+-------------+--------
x.. ... | 2 0 0 | 3 * * * * | 1 1 1 0 0 0 | 1 1 1 0
oo.3oo.&#x | 1 1 0 | * 3 * * * | 0 2 0 1 0 0 | 1 0 2 0
o.o3o.o&#x | 1 0 1 | * * 3 * * | 0 0 2 1 0 0 | 0 1 2 0
.oo3.oo&#x | 0 1 1 | * * * 3 * | 0 0 0 1 2 0 | 0 0 2 1
..x ... | 0 0 2 | * * * * 3 | 0 0 1 0 1 1 | 0 1 1 1
-----------+-------+-----------+-------------+--------
x..3o.. | 3 0 0 | 3 0 0 0 0 | 1 * * * * * | 1 1 0 0
xo. ...&#x | 2 1 0 | 1 2 0 0 0 | * 3 * * * * | 1 0 1 0
x.x ...&#x | 2 0 2 | 1 0 2 0 1 | * * 3 * * * | 0 1 1 0
ooo3ooo&#x | 1 1 1 | 0 1 1 1 0 | * * * 3 * * | 0 0 2 0
.ox ...&#x | 0 1 2 | 0 0 0 2 1 | * * * * 3 * | 0 0 1 1
..x3..o | 0 0 3 | 0 0 0 0 3 | * * * * * 1 | 0 1 0 1
-----------+-------+-----------+-------------+--------
xo.3oo.&#x ♦ 3 1 0 | 3 3 0 0 0 | 1 3 0 0 0 0 | 1 * * *
x.x3o.o&#x ♦ 3 0 3 | 3 0 3 0 3 | 1 0 3 0 0 1 | * 1 * *
xox ...&#x ♦ 2 1 2 | 1 2 2 2 1 | 0 1 1 2 1 0 | * * 3 *
.ox3.oo&#x ♦ 0 1 3 | 0 0 0 3 3 | 0 0 0 0 3 1 | * * * 1
line || squippy → height = sqrt(5/8) = 0.790569
shear = 1/sqrt(8) = 0.353553
2 * * | 1 1 2 0 0 0 | 1 2 2 1 0 0 0 | 2 1 1 0
* 1 * ♦ 0 2 0 4 0 0 | 1 0 4 0 2 2 0 | 2 0 2 1
* * 4 | 0 0 1 1 1 1 | 0 1 1 1 1 1 1 | 1 1 1 1
--------+-------------+---------------+--------
2 0 0 | 1 * * * * * | 1 2 0 0 0 0 0 | 2 1 0 0
1 1 0 | * 2 * * * * | 1 0 2 0 0 0 0 | 2 0 1 0
1 0 1 | * * 4 * * * | 0 1 1 1 0 0 0 | 1 1 1 0
0 1 1 | * * * 4 * * | 0 0 1 0 1 1 0 | 1 0 1 1
0 0 2 | * * * * 2 * | 0 1 0 0 1 0 1 | 1 1 0 1 para
0 0 2 | * * * * * 2 | 0 0 0 1 0 1 1 | 0 1 1 1 ortho
--------+-------------+---------------+--------
2 1 0 | 1 2 0 0 0 0 | 1 * * * * * * | 2 0 0 0
2 0 2 | 1 0 2 0 1 0 | * 2 * * * * * | 1 1 0 0
1 1 1 | 0 1 1 1 0 0 | * * 4 * * * * | 1 0 1 0
1 0 2 | 0 0 2 0 0 1 | * * * 2 * * * | 0 1 1 0
0 1 2 | 0 0 0 2 1 0 | * * * * 2 * * | 1 0 0 1
0 1 2 | 0 0 0 2 0 1 | * * * * * 2 * | 0 0 1 1
0 0 4 | 0 0 0 0 2 2 | * * * * * * 1 | 0 1 0 1
--------+-------------+---------------+--------
♦ 2 1 2 | 1 2 2 2 1 0 | 1 1 2 0 1 0 0 | 2 * * *
♦ 2 0 4 | 1 0 4 0 2 2 | 0 2 0 2 0 0 1 | * 1 * *
♦ 1 1 2 | 0 1 2 2 0 1 | 0 0 2 1 0 1 0 | * * 2 *
♦ 0 1 4 | 0 0 0 4 2 2 | 0 0 0 0 2 2 1 | * * * 1
xoo xox&#x → height(1,2) = 1/sqrt(2) = 0.707107 height(1,3) = height(2,3) = sqrt(3)/2 = 0.866025 o.. o.. | 4 * * | 1 1 1 1 0 0 | 1 1 1 1 1 1 0 | 1 1 1 1 .o. .o. | * 1 * ♦ 0 0 4 0 2 0 | 0 2 2 0 0 4 1 | 1 0 2 2 ..o ..o | * * 2 | 0 0 0 2 1 1 | 0 0 0 1 2 2 1 | 0 1 1 2 -----------+-------+-------------+---------------+-------- x.. ... | 2 0 0 | 2 * * * * * | 1 1 0 1 0 0 0 | 1 1 1 0 ... x.. | 2 0 0 | * 2 * * * * | 1 0 1 0 1 0 0 | 1 1 0 1 oo. oo.&#x | 1 1 0 | * * 4 * * * | 0 1 1 0 0 1 0 | 1 0 1 1 o.o o.o&#x | 1 0 1 | * * * 4 * * | 0 0 0 1 1 1 0 | 0 1 1 1 .oo .oo&#x | 0 1 1 | * * * * 2 * | 0 0 0 0 0 2 1 | 0 0 1 2 ... ..x | 0 0 2 | * * * * * 1 | 0 0 0 0 2 0 1 | 0 1 0 2 -----------+-------+-------------+---------------+-------- x.. x.. | 4 0 0 | 2 2 0 0 0 0 | 1 * * * * * * | 1 1 0 0 xo. ...&#x | 2 1 0 | 1 0 2 0 0 0 | * 2 * * * * * | 1 0 1 0 ... xo.&#x | 2 1 0 | 0 1 2 0 0 0 | * * 2 * * * * | 1 0 0 1 x.o ...&#x | 2 0 1 | 1 0 0 2 0 0 | * * * 2 * * * | 0 1 1 0 ... x.x&#x | 2 0 2 | 0 1 0 2 0 1 | * * * * 2 * * | 0 1 0 1 ooo ooo&#x | 1 1 1 | 0 0 1 1 1 0 | * * * * * 4 * | 0 0 1 1 ... .ox&#x | 0 1 2 | 0 0 0 0 2 1 | * * * * * * 1 | 0 0 0 2 -----------+-------+-------------+---------------+-------- xo. xo.&#x ♦ 4 1 0 | 2 2 4 0 0 0 | 1 2 2 0 0 0 0 | 1 * * * x.o x.x&#x ♦ 4 0 2 | 2 2 0 4 0 1 | 1 0 0 2 2 0 0 | * 1 * * xoo ...&#x ♦ 2 1 1 | 1 0 2 2 1 0 | 0 1 0 1 0 2 0 | * * 2 * ... xox&#x ♦ 2 1 2 | 0 1 2 2 2 1 | 0 0 1 0 1 2 1 | * * * 2
oxxx&#x → height(1,2) = height(1,3) = height(1,4) = sqrt(3)/2 = 0.866025 height(2,3) = height(2,4) = height(3,4) = 1 o... | 11 * * * ♦ 2 2 2 0 0 0 0 0 0 | 1 2 2 1 2 1 0 0 0 0 | 1 2 1 1 0 .o.. | * 2 * * | 1 0 0 1 1 1 0 0 0 | 1 1 1 0 0 0 1 1 1 0 | 1 1 1 0 1 ..o. | * * 2 * | 0 1 0 0 1 0 1 1 0 | 0 1 0 1 1 0 1 1 0 1 | 1 1 0 1 1 ...o | * * * 2 | 0 0 1 0 0 1 0 1 1 | 0 0 1 0 1 1 0 1 1 1 | 0 1 1 1 1 --------+---------+-------------------+---------------------+---------- oo..&#x | 1 1 0 0 | 2 * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0 o.o.&#x | 1 0 1 0 | * 2 * * * * * * * | 0 1 0 1 1 0 0 0 0 0 | 1 1 0 1 0 o..o&#x | 1 0 0 1 | * * 2 * * * * * * | 0 0 1 0 1 1 0 0 0 0 | 0 1 1 1 0 .x.. | 0 2 0 0 | * * * 1 * * * * * | 1 0 0 0 0 0 1 0 1 0 | 1 0 1 0 1 .oo.&#x | 0 1 1 0 | * * * * 2 * * * * | 0 1 0 0 0 0 1 1 0 0 | 1 1 0 0 1 .o.o&#x | 0 1 0 1 | * * * * * 2 * * * | 0 0 1 0 0 0 0 1 1 0 | 0 1 1 0 1 ..x. | 0 0 2 0 | * * * * * * 1 * * | 0 0 0 1 0 0 1 0 0 1 | 1 0 0 1 1 ..oo&#x | 0 0 1 1 | * * * * * * * 2 * | 0 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1 ...x | 0 0 0 2 | * * * * * * * * 1 | 0 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1 --------+---------+-------------------+---------------------+---------- ox..&#x | 1 2 0 0 | 2 0 0 1 0 0 0 0 0 | 1 * * * * * * * * * | 1 0 1 0 0 ooo.&#x | 1 1 1 0 | 1 1 0 0 1 0 0 0 0 | * 2 * * * * * * * * | 1 1 0 0 0 oo.o&#x | 1 1 0 1 | 1 0 1 0 0 1 0 0 0 | * * 2 * * * * * * * | 0 1 1 0 0 o.x.&#x | 1 0 2 0 | 0 2 0 0 0 0 1 0 0 | * * * 1 * * * * * * | 1 0 0 1 0 o.oo&#x | 1 0 1 1 | 0 1 1 0 0 0 0 1 0 | * * * * 2 * * * * * | 0 1 0 1 0 o..x&#x | 1 0 0 2 | 0 0 2 0 0 0 0 0 1 | * * * * * 1 * * * * | 0 0 1 1 0 .xx.&#x | 0 2 2 0 | 0 0 0 1 2 0 1 0 0 | * * * * * * 1 * * * | 1 0 0 0 1 .ooo&#x | 0 1 1 1 | 0 0 0 0 1 1 0 1 0 | * * * * * * * 2 * * | 0 1 0 0 1 .x.x&#x | 0 2 0 2 | 0 0 0 1 0 2 0 0 1 | * * * * * * * * 1 * | 0 0 1 0 1 ..xx&#x | 0 0 2 2 | 0 0 0 0 0 0 1 2 1 | * * * * * * * * * 1 | 0 0 0 1 1 --------+---------+-------------------+---------------------+---------- oxx.&#x ♦ 1 2 2 0 | 2 2 0 1 2 0 1 0 0 | 1 2 0 1 0 0 1 0 0 0 | 1 * * * * oooo&#x ♦ 1 1 1 1 | 1 1 1 0 1 1 0 1 0 | 0 1 1 0 1 0 0 1 0 0 | * 2 * * * ox.x&#x ♦ 1 2 0 2 | 2 0 2 1 0 2 0 0 1 | 1 0 2 0 0 1 0 0 1 0 | * * 1 * * o.xx&#x ♦ 1 0 2 2 | 0 2 2 0 0 0 1 2 1 | 0 0 0 1 2 1 0 0 0 1 | * * * 1 * .xxx&#x ♦ 0 2 2 2 | 0 0 0 1 2 2 1 2 1 | 0 0 0 0 0 0 1 2 1 1 | * * * * 1
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