Acronym | bidrap, K-4.8 |
Name |
bidiminished rectified pentachoron, antiduowedge, square - tetrahedral wedge, digonal gyrobicupolaic ring, {4} || tet, line || ortho trip |
Segmentochoron display |
©(these providing possible orientations: as "squippy || {3}", as "tet || {4}", resp. as "trip || ortho line") |
Circumradius | sqrt(3/5) = 0.774597 |
Lace city in approx. ASCII-art |
x o o x x x |
Dihedral angles |
|
Face vector | 8, 18, 17, 7 |
Confer |
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External links |
The rap can be considered as tet || oct. Now diminish the bottom oct at both opposing tips down to the equatorial square. At the top tet the same diminishings just scratch at the pair of opposing edges. Either diminishing chops off a trippy.
Incidence matrix according to Dynkin symbol
xxo oxx&#x → height(1,2) = height(2,3) = sqrt(3)/2 = 0.866025 height(1,3) = 1/sqrt(2) = 0.707107 o.. o.. | 2 * * | 1 2 2 0 0 0 0 | 2 1 2 1 2 0 0 0 | 1 1 2 1 0 .o. .o. | * 4 * | 0 1 0 1 1 1 0 | 1 1 0 0 1 1 1 1 | 1 0 1 1 1 ..o ..o | * * 2 | 0 0 2 0 0 2 1 | 0 0 1 2 2 0 1 2 | 0 1 1 2 1 -----------+-------+---------------+-----------------+---------- x.. ... | 2 0 0 | 1 * * * * * * | 2 0 2 0 0 0 0 0 | 1 1 2 0 0 oo. oo.&#x | 1 1 0 | * 4 * * * * * | 1 1 0 0 1 0 0 0 | 1 0 1 1 0 o.o o.o&#x | 1 0 1 | * * 4 * * * * | 0 0 1 1 1 0 0 0 | 0 1 1 1 0 .x. ... | 0 2 0 | * * * 2 * * * | 1 0 0 0 0 1 1 0 | 1 0 1 0 1 ... .x. | 0 2 0 | * * * * 2 * * | 0 1 0 0 0 1 0 1 | 1 0 0 1 1 .oo .oo&#x | 0 1 1 | * * * * * 4 * | 0 0 0 0 1 0 1 1 | 0 0 1 1 1 ... ..x | 0 0 2 | * * * * * * 1 | 0 0 0 2 0 0 0 2 | 0 1 0 2 1 -----------+-------+---------------+-----------------+---------- xx. ...&#x | 2 2 0 | 1 2 0 1 0 0 0 | 2 * * * * * * * | 1 0 1 0 0 ... ox.&#x | 1 2 0 | 0 2 0 0 1 0 0 | * 2 * * * * * * | 1 0 0 1 0 x.o ...&#x | 2 0 1 | 1 0 2 0 0 0 0 | * * 2 * * * * * | 0 1 1 0 0 ... o.x&#x | 1 0 2 | 0 0 2 0 0 0 1 | * * * 2 * * * * | 0 1 0 1 0 ooo ooo&#x | 1 1 1 | 0 1 1 0 0 1 0 | * * * * 4 * * * | 0 0 1 1 0 .x. .x. | 0 4 0 | 0 0 0 2 2 0 0 | * * * * * 1 * * | 1 0 0 0 1 .xo ...&#x | 0 2 1 | 0 0 0 1 0 2 0 | * * * * * * 2 * | 0 0 1 0 1 ... .xx&#x | 0 2 2 | 0 0 0 0 1 2 1 | * * * * * * * 2 | 0 0 0 1 1 -----------+-------+---------------+-----------------+---------- xx. ox.&#x ♦ 2 4 0 | 1 4 0 2 2 0 0 | 2 2 0 0 0 1 0 0 | 1 * * * * x.o o.x&#x ♦ 2 0 2 | 1 0 4 0 0 0 1 | 0 0 2 2 0 0 0 0 | * 1 * * * xxo ...&#x ♦ 2 2 1 | 1 2 2 1 0 2 0 | 1 0 1 0 2 0 1 0 | * * 2 * * ... oxx&#x ♦ 1 2 2 | 0 2 2 0 1 2 1 | 0 1 0 1 2 0 0 1 | * * * 2 * .xo .xx&#x ♦ 0 4 2 | 0 0 0 2 2 4 1 | 0 0 0 0 0 1 2 2 | * * * * 1
x(xo) x(ox)&#x → height = sqrt(5/8) = 0.790569
({4} || tet)
o(..) o(..) | 4 * | 2 2 0 0 | 1 2 2 1 0 | 2 2 0
.(o.) .(o.) & | * 4 | 0 2 1 2 | 0 2 1 2 3 | 1 3 1
-----------------+-----+---------+-----------+------
x(..) .(..) & | 2 0 | 4 * * * | 1 1 1 0 0 | 2 1 0
o(o.) o(o.)&#x & | 1 1 | * 8 * * | 0 1 1 1 0 | 1 2 0
.(x.) .(..) & | 0 2 | * * 2 * | 0 2 0 0 2 | 1 2 1
.(oo) .(oo)&#x | 0 2 | * * * 4 | 0 0 0 1 2 | 0 2 1
-----------------+-----+---------+-----------+------
x(..) x(..) | 4 0 | 4 0 0 0 | 1 * * * * | 2 0 0
x(x.) .(..) & | 2 2 | 1 2 1 0 | * 4 * * * | 1 1 0
.(..) x(o.) & | 2 1 | 1 2 0 0 | * * 4 * * | 1 1 0
o(oo) o(oo)&#x | 1 2 | 0 2 0 1 | * * * 4 * | 0 2 0
.(xo) .(..)&#x & | 0 3 | 0 0 1 2 | * * * * 4 | 0 1 1
-----------------+-----+---------+-----------+------
x(x.) x(o.)&#x & ♦ 4 2 | 4 4 1 0 | 1 2 2 0 0 | 2 * *
x(xo) .(..)&#x & ♦ 2 3 | 1 4 1 2 | 0 1 1 2 1 | * 4 *
.(xo) .(ox)&#x ♦ 0 4 | 0 0 2 4 | 0 0 0 0 4 | * * 1
oqo ooo&#xt || snub(xx xx&#x) → height = sqrt(5/8) = 0.790569 ({4} || tet) o.. o.. .. .. | 1 * * * * | 2 2 0 0 0 0 0 0 0 0 | 1 2 2 1 0 0 0 0 0 0 | 2 2 0 0 .o. .o. .. .. | * 2 * * * | 1 0 1 1 1 0 0 0 0 0 | 1 1 1 0 1 1 1 0 0 0 | 2 1 1 0 ..o ..o .. .. | * * 1 * * | 0 0 2 0 0 2 0 0 0 0 | 1 0 0 0 2 2 0 1 0 0 | 2 0 2 0 ... ... demi(o. o. ) | * * * 2 * | 0 1 0 1 0 0 1 1 1 0 | 0 1 1 1 1 0 1 0 2 1 | 1 2 1 1 ... ... demi(.o .o ) | * * * * 2 | 0 0 0 0 1 1 0 1 1 1 | 0 0 1 0 1 1 1 1 1 2 | 1 1 2 1 -----------------------------+-----------+---------------------+---------------------+-------- oo. oo.&#x .. .. | 1 1 0 0 0 | 2 * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 | 2 1 0 0 o.. o.. || demi(o. o. ) | 1 0 0 1 0 | * 2 * * * * * * * * | 0 1 1 1 0 0 0 0 0 0 | 1 2 0 0 .oo .oo&#x .. .. | 0 1 1 0 0 | * * 2 * * * * * * * | 1 0 0 0 1 1 0 0 0 0 | 2 0 1 0 .o. .o. || demi(o. o. ) | 0 1 0 1 0 | * * * 2 * * * * * * | 0 1 0 0 1 0 1 0 0 0 | 1 1 1 0 .o. .o. || demi(.o .o ) | 0 1 0 0 1 | * * * * 2 * * * * * | 0 0 1 0 0 1 1 0 0 0 | 1 1 1 0 ..o ..o || demi(.o .o ) | 0 0 1 0 1 | * * * * * 2 * * * * | 0 0 0 0 1 1 0 1 0 0 | 1 0 2 0 ... ... s.2s. | 0 0 0 2 0 | * * * * * * 1 * * * | 0 0 0 1 0 0 0 0 2 0 | 0 2 0 1 ... ... snub(xx ..&#x) | 0 0 0 1 1 | * * * * * * * 2 * * | 0 0 1 0 1 0 0 0 1 1 | 1 1 1 1 ... ... snub(.. xx&#x) | 0 0 0 1 1 | * * * * * * * * 2 * | 0 0 0 0 0 0 1 0 1 1 | 0 1 1 1 ... ... .s2.s | 0 0 0 0 2 | * * * * * * * * * 1 | 0 0 0 0 0 0 0 1 0 2 | 0 0 2 1 -----------------------------+-----------+---------------------+---------------------+-------- oqo ...&#xt .. .. | 1 2 1 0 0 | 2 0 2 0 0 0 0 0 0 0 | 1 * * * * * * * * * | 2 0 0 0 oo. oo.&#x || demi(o. o. ) | 1 1 0 1 0 | 1 1 0 1 0 0 0 0 0 0 | * 2 * * * * * * * * | 1 1 0 0 oo. oo.&#x || snub(xx ..&#x) | 1 1 0 1 1 | 1 1 0 0 1 0 0 1 0 0 | * * 2 * * * * * * * | 1 1 0 0 o.. o.. || s.2s. | 1 0 0 2 0 | 0 2 0 0 0 0 1 0 0 0 | * * * 1 * * * * * * | 0 2 0 0 .oo .oo&#x || snub(xx ..&#x) | 0 1 1 1 1 | 0 0 1 1 0 1 0 1 0 0 | * * * * 2 * * * * * | 1 0 1 0 .oo .oo&#x || demi(.o .o ) | 0 1 1 0 1 | 0 0 1 0 1 1 0 0 0 0 | * * * * * 2 * * * * | 1 0 1 0 .o. .o. || snub(.. xx&#x) | 0 1 0 1 1 | 0 0 0 1 1 0 0 0 1 0 | * * * * * * 2 * * * | 0 1 1 0 ..o ..o || .s2.s | 0 0 1 0 2 | 0 0 0 0 0 2 0 0 0 1 | * * * * * * * 1 * * | 0 0 2 0 ... ... so2so&#x | 0 0 0 2 1 | 0 0 0 0 0 0 1 1 1 0 | * * * * * * * * 2 * | 0 1 0 1 ... ... os2os&#x | 0 0 0 1 2 | 0 0 0 0 0 0 0 1 1 1 | * * * * * * * * * 2 | 0 0 1 1 -----------------------------+-----------+---------------------+---------------------+-------- oqo ...&#xt || snub(xx ..&#x) ♦ 1 2 1 1 1 | 2 1 2 1 1 1 0 1 0 0 | 1 1 1 0 1 1 0 0 0 0 | 2 * * * oo. oo.&#x || so2so&#x ♦ 1 1 0 2 1 | 1 2 0 1 1 0 1 1 1 0 | 0 1 1 1 0 0 1 0 1 0 | * 2 * * .oo .oo&#x || os2os&#x ♦ 0 1 1 1 2 | 0 0 1 1 1 2 0 1 1 1 | 0 0 0 0 1 1 1 1 0 1 | * * 2 * ... ... snub(xx xx&#x) ♦ 0 0 0 2 2 | 0 0 0 0 0 0 1 2 2 1 | 0 0 0 0 0 0 0 0 2 2 | * * * 1
{3} || squippy → height = sqrt(5/8) = 0.790569
2 * * * * | 1 1 1 1 0 0 0 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 0 0 | 1 1 1 1 0 0
* 1 * * * | 0 2 0 0 2 1 0 0 0 0 0 | 1 0 0 2 2 0 1 2 0 0 0 0 | 1 1 0 2 1 0
* * 2 * * | 0 0 1 0 1 0 1 1 1 0 0 | 0 1 0 1 0 1 1 1 1 1 1 0 | 1 0 1 1 1 1
* * * 1 * | 0 0 0 0 0 1 0 2 0 2 0 | 0 0 0 0 2 0 0 2 1 0 2 1 | 0 1 0 2 1 1
* * * * 2 | 0 0 0 1 0 0 0 0 1 1 1 | 0 0 1 0 1 1 0 0 0 1 1 1 | 0 1 1 1 0 1
------------+-----------------------+-------------------------+------------
2 0 0 0 0 | 1 * * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
1 1 0 0 0 | * 2 * * * * * * * * * | 1 0 0 1 1 0 0 0 0 0 0 0 | 1 1 0 1 0 0
1 0 1 0 0 | * * 2 * * * * * * * * | 0 1 0 1 0 1 0 0 0 0 0 0 | 1 0 1 1 0 0
1 0 0 0 1 | * * * 2 * * * * * * * | 0 0 1 0 1 1 0 0 0 0 0 0 | 0 1 1 1 0 0
0 1 1 0 0 | * * * * 2 * * * * * * | 0 0 0 1 0 0 1 1 0 0 0 0 | 1 0 0 1 1 0
0 1 0 1 0 | * * * * * 1 * * * * * | 0 0 0 0 2 0 0 2 0 0 0 0 | 0 1 0 2 1 0
0 0 2 0 0 | * * * * * * 1 * * * * | 0 1 0 0 0 0 1 0 1 1 0 0 | 1 0 1 0 1 1
0 0 1 1 0 | * * * * * * * 2 * * * | 0 0 0 0 0 0 0 1 1 0 1 0 | 0 0 0 1 1 1
0 0 1 0 1 | * * * * * * * * 2 * * | 0 0 0 0 0 1 0 0 0 1 1 0 | 0 0 1 1 0 1
0 0 0 1 1 | * * * * * * * * * 2 * | 0 0 0 0 1 0 0 0 0 0 1 1 | 0 1 0 1 0 1
0 0 0 0 2 | * * * * * * * * * * 1 | 0 0 1 0 0 0 0 0 0 1 0 1 | 0 1 1 0 0 1
------------+-----------------------+-------------------------+------------
2 1 0 0 0 | 1 2 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * | 1 1 0 0 0 0
2 0 2 0 0 | 1 0 2 0 0 0 1 0 0 0 0 | * 1 * * * * * * * * * * | 1 0 1 0 0 0
2 0 0 0 2 | 1 0 0 2 0 0 0 0 0 0 1 | * * 1 * * * * * * * * * | 0 1 1 0 0 0
1 1 1 0 0 | 0 1 1 0 1 0 0 0 0 0 0 | * * * 2 * * * * * * * * | 1 0 0 1 0 0
1 1 0 1 1 | 0 1 0 1 0 1 0 0 0 1 0 | * * * * 2 * * * * * * * | 0 1 0 1 0 0
1 0 1 0 1 | 0 0 1 1 0 0 0 0 1 0 0 | * * * * * 2 * * * * * * | 0 0 1 1 0 0
0 1 2 0 0 | 0 0 0 0 2 0 1 0 0 0 0 | * * * * * * 1 * * * * * | 1 0 0 0 1 0
0 1 1 1 0 | 0 0 0 0 1 1 0 1 0 0 0 | * * * * * * * 2 * * * * | 0 0 0 1 1 0
0 0 2 1 0 | 0 0 0 0 0 0 1 2 0 0 0 | * * * * * * * * 1 * * * | 0 0 0 0 1 1
0 0 2 0 2 | 0 0 0 0 0 0 1 0 2 0 1 | * * * * * * * * * 1 * * | 0 0 1 0 0 1
0 0 1 1 1 | 0 0 0 0 0 0 0 1 1 1 0 | * * * * * * * * * * 2 * | 0 0 0 1 0 1
0 0 0 1 2 | 0 0 0 0 0 0 0 0 0 2 1 | * * * * * * * * * * * 1 | 0 1 0 0 0 1
------------+-----------------------+-------------------------+------------
♦ 2 1 2 0 0 | 1 2 2 0 2 0 1 0 0 0 0 | 1 1 0 2 0 0 1 0 0 0 0 0 | 1 * * * * *
♦ 2 1 0 1 2 | 1 2 0 2 0 1 0 0 0 2 1 | 1 0 1 0 2 0 0 0 0 0 0 1 | * 1 * * * *
♦ 2 0 2 0 2 | 1 0 2 2 0 0 1 0 2 0 1 | 0 1 1 0 0 2 0 0 0 1 0 0 | * * 1 * * *
♦ 1 1 1 1 1 | 0 1 1 1 1 1 0 1 1 1 0 | 0 0 0 1 1 1 0 1 0 0 1 0 | * * * 2 * *
♦ 0 1 2 1 0 | 0 0 0 0 2 1 1 2 0 0 0 | 0 0 0 0 0 0 1 2 1 0 0 0 | * * * * 1 *
♦ 0 0 2 1 2 | 0 0 0 0 0 0 1 2 2 2 1 | 0 0 0 0 0 0 0 0 1 1 2 1 | * * * * * 1
x(ox) o(xx)&#x → height = sqrt(5/12) = 0.645497
(line || ortho trip)
o(..) o(..) | 2 * * | 1 2 2 0 0 0 0 | 2 2 1 2 1 0 0 0 | 1 1 2 1 0
.(o.) .(o.) | * 2 * | 0 2 0 1 2 0 0 | 1 0 2 2 0 1 2 0 | 1 0 1 2 1
.(.o) .(.o) | * * 4 | 0 0 1 0 1 1 1 | 0 1 0 1 1 1 1 1 | 0 1 1 1 1
---------------+-------+---------------+-----------------+----------
x(..) .(..) | 2 0 0 | 1 * * * * * * | 2 2 0 0 0 0 0 0 | 1 1 2 0 0
o(o.) o(o.)&#x | 1 1 0 | * 4 * * * * * | 1 0 1 1 0 0 0 0 | 1 0 1 1 0
o(.o) o(.o)&#x | 1 0 1 | * * 4 * * * * | 0 1 0 1 1 0 0 0 | 0 1 1 1 0
.(..) .(x.) | 0 2 0 | * * * 1 * * * | 0 0 2 0 0 0 2 0 | 1 0 0 2 1
.(oo) .(oo)&#x | 0 1 1 | * * * * 4 * * | 0 0 0 1 0 1 1 0 | 0 0 1 1 1
.(.x) .(..) | 0 0 2 | * * * * * 2 * | 0 1 0 0 0 1 0 1 | 0 1 1 0 1
.(..) .(.x) | 0 0 2 | * * * * * * 2 | 0 0 0 0 1 0 1 1 | 0 1 0 1 1
---------------+-------+---------------+-----------------+----------
x(o.) .(..)&#x | 2 1 0 | 1 2 0 0 0 0 0 | 2 * * * * * * * | 1 0 1 0 0
x(.x) .(..)&#x | 2 0 2 | 1 0 2 0 0 1 0 | * 2 * * * * * * | 0 1 1 0 0
.(..) o(x.)&#x | 1 2 0 | 0 2 0 1 0 0 0 | * * 2 * * * * * | 1 0 0 1 0
o(oo) o(oo)&#x | 1 1 1 | 0 1 1 0 1 0 0 | * * * 4 * * * * | 0 0 1 1 0
.(..) o(.x)&#x | 1 0 2 | 0 0 2 0 0 0 1 | * * * * 2 * * * | 0 1 0 1 0
.(ox) .(..)&#x | 0 1 2 | 0 0 0 0 2 1 0 | * * * * * 2 * * | 0 0 1 0 1
.(..) .(xx)&#x | 0 2 2 | 0 0 0 1 2 0 1 | * * * * * * 2 * | 0 0 0 1 1
.(.x) .(.x) | 0 0 4 | 0 0 0 0 0 2 2 | * * * * * * * 1 | 0 1 0 0 1
---------------+-------+---------------+-----------------+----------
x(o.) o(x.)&#x ♦ 2 2 0 | 1 4 0 1 0 0 0 | 2 0 2 0 0 0 0 0 | 1 * * * *
x(.x) o(.x)&#x ♦ 2 0 4 | 1 0 4 0 0 2 2 | 0 2 0 0 2 0 0 1 | * 1 * * *
x(ox) .(..)&#x ♦ 2 1 2 | 1 2 2 0 2 1 0 | 1 1 0 2 0 1 0 0 | * * 2 * *
.(..) o(xx)&#x ♦ 1 2 2 | 0 2 2 1 2 0 1 | 0 0 1 2 1 0 1 0 | * * * 2 *
.(ox) .(xx)&#x ♦ 0 2 4 | 0 0 0 1 4 2 2 | 0 0 0 0 0 2 2 1 | * * * * 1
( xo.&#x, xo.&#x, ..x )&#x → height = sqrt(5/12) = 0.645497
(line || ortho trip)
( o.. , ... , ... ) & | 4 * * | 1 1 1 1 0 0 0 | 1 1 1 1 1 1 0 0 | 1 1 1 1 0
( .o. , ... , ... ) & | * 2 * | 0 2 0 0 1 2 0 | 1 0 2 2 0 0 2 1 | 1 2 1 0 1
( ... , ... , ..o ) | * * 2 | 0 0 0 2 0 2 1 | 0 0 0 2 1 2 1 2 | 0 1 2 1 1
-----------------------------+-------+---------------+-----------------+----------
( x.. , ... , ... ) & | 2 0 0 | 2 * * * * * * | 1 1 0 0 0 1 0 0 | 1 0 1 1 0
( oo.&#x, ... , ... ) & | 1 1 0 | * 4 * * * * * | 1 0 1 1 0 0 0 0 | 1 1 1 0 0
( o.. , o.. , ... )&#x & | 2 0 0 | * * 2 * * * * | 0 1 1 0 1 0 0 0 | 1 1 0 1 0
( o.. , ... , ..o )&#x & | 1 0 1 | * * * 4 * * * | 0 0 0 1 1 1 0 0 | 0 1 1 1 0
( .o. , .o. , ... )&#x | 0 2 0 | * * * * 1 * * | 0 0 2 0 0 0 2 0 | 1 2 0 0 1
( .o. , ... , ..o )&#x & | 0 1 1 | * * * * * 4 * | 0 0 0 1 0 0 1 1 | 0 1 1 0 1
( ... , ... , ..x ) | 0 0 2 | * * * * * * 1 | 0 0 0 0 0 2 0 2 | 0 0 2 1 1
-----------------------------+-------+---------------+-----------------+----------
( xo.&#x, ... , ... ) & | 2 1 0 | 1 2 0 0 0 0 0 | 2 * * * * * * * | 1 0 1 0 0
( x.. , x.. , ... )&#x | 4 0 0 | 2 0 2 0 0 0 0 | * 1 * * * * * * | 1 0 0 1 0
( oo.&#x, oo.&#x, ... )&#x | 2 2 0 | 0 2 1 0 1 0 0 | * * 2 * * * * * | 1 1 0 0 0
( oo.&#x, ... , ..o )&#x & | 1 1 1 | 0 1 0 1 0 1 0 | * * * 4 * * * * | 0 1 1 0 0
( o.. , o.. , ..o )&#x | 2 0 1 | 0 0 1 2 0 0 0 | * * * * 2 * * * | 0 1 0 1 0
( x.. , ... , ..x )&#x & | 2 0 2 | 1 0 0 2 0 0 1 | * * * * * 2 * * | 0 0 1 1 0
( .o. , .o. , ..o )&#x & | 0 2 1 | 0 0 0 0 1 2 0 | * * * * * * 2 * | 0 1 0 0 1
( .o. , ... , ..x )&#x & | 0 1 2 | 0 0 0 0 0 2 1 | * * * * * * * 2 | 0 0 1 0 1
-----------------------------+-------+---------------+-----------------+----------
( xo.&#x, xo.&#x, ... )&#x ♦ 4 2 0 | 2 4 2 0 1 0 0 | 2 1 2 0 0 0 0 0 | 1 * * * *
( oo.&#x, oo.&#x, ..o )&#x ♦ 2 2 1 | 0 2 1 2 1 2 0 | 0 0 1 2 1 0 1 0 | * 2 * * *
( xo.&#x, ... , ..x )&#x & ♦ 2 1 2 | 1 2 0 2 0 2 1 | 1 0 0 2 0 1 0 1 | * * 2 * *
( x.. , x.. , ..x )&#x ♦ 4 0 2 | 2 0 2 4 0 0 1 | 0 1 0 0 2 2 0 0 | * * * 1 *
( .o. , .o. , ..x )&#x ♦ 0 2 2 | 0 0 0 0 1 4 1 | 0 0 0 0 0 0 2 2 | * * * * 1
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