digonal-square duoantiwedge,
square prism atop bidual square prism
©
in approx. ASCII-art
4 4 = o o4x (square) P P = x x4o (gyro {4}-prism) 4
- more general:
- n/d-daf
- related segmentotera:
- cubaope
- general polytopal classes:
- segmentotera scaliform
links
| Acronym | squiddaf |
| Name |
square duoantifastegium, digonal-square duoantiwedge, square prism atop bidual square prism |
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| Circumradius | sqrt[(5+sqrt(2))/8] = 0.895420 |
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Lace city in approx. ASCII-art |
4 4 = o o4x (square) P P = x x4o (gyro {4}-prism) 4 |
| Face vector | 16, 56, 76, 46, 12 |
| Confer |
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External links |
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This polyteron well can be obtained from cubaope. For if at its base ope both oct bases in turn would get diminished down to a diametral square, then that whole base would become a cube too (the bidual {4}-prism).
Incidence matrix according to Dynkin symbol
xo ox xo4ox&#x → height = sqrt[(sqrt(2)-1)/2] = 0.455090
({4}-prism || bidual {4}-prism)
o. o. o.4o. | 8 * | 1 2 4 0 0 | 2 1 4 2 4 2 0 0 | 1 2 4 2 2 1 2 0 | 2 1 2 1
.o .o .o4.o | * 8 | 0 0 4 1 2 | 0 0 2 4 2 4 2 1 | 0 2 1 2 2 4 2 1 | 1 2 1 2
---------------+-----+------------+---------------------+-----------------+--------
x. .. .. .. | 2 0 | 4 * * * * | 2 0 4 0 0 0 0 0 | 1 2 4 2 0 0 0 0 | 2 1 2 0
.. .. x. .. | 2 0 | * 8 * * * | 1 1 0 0 2 0 0 0 | 1 0 2 0 1 0 2 0 | 1 0 2 1
oo oo oo4oo&#x | 1 1 | * * 32 * * | 0 0 1 1 1 1 0 0 | 0 1 1 1 1 1 1 0 | 1 1 1 1
.. .x .. .. | 0 2 | * * * 4 * | 0 0 0 4 0 0 2 0 | 0 2 0 0 2 4 0 1 | 1 2 0 2
.. .. .. .x | 0 2 | * * * * 8 | 0 0 0 0 0 2 1 1 | 0 0 0 1 0 2 2 1 | 0 1 1 2
---------------+-----+------------+---------------------+-----------------+--------
x. .. x. .. | 4 0 | 2 2 0 0 0 | 4 * * * * * * * | 1 0 2 0 0 0 0 0 | 1 0 2 0
.. .. x.4o. | 4 0 | 0 4 0 0 0 | * 2 * * * * * * | 1 0 0 0 0 0 2 0 | 0 0 2 1
xo .. .. ..&#x | 2 1 | 1 0 2 0 0 | * * 16 * * * * * | 0 1 1 1 0 0 0 0 | 1 1 1 0
.. ox .. ..&#x | 1 2 | 0 0 2 1 0 | * * * 16 * * * * | 0 1 0 0 1 1 0 0 | 1 1 0 1
.. .. xo ..&#x | 2 1 | 0 1 2 0 0 | * * * * 16 * * * | 0 0 1 0 1 0 1 0 | 1 0 1 1
.. .. .. ox&#x | 1 2 | 0 0 2 0 1 | * * * * * 16 * * | 0 0 0 1 0 1 1 0 | 0 1 1 1
.. .x .. .x | 0 4 | 0 0 0 2 2 | * * * * * * 4 * | 0 0 0 0 0 2 0 1 | 0 1 0 2
.. .. .o4.x | 0 4 | 0 0 0 0 4 | * * * * * * * 2 | 0 0 0 0 0 0 2 1 | 0 0 1 2
---------------+-----+------------+---------------------+-----------------+--------
x. .. x.4o. ♦ 8 0 | 4 8 0 0 0 | 4 2 0 0 0 0 0 0 | 1 * * * * * * * | 0 0 2 0
xo ox .. ..&#x ♦ 2 2 | 1 0 4 1 0 | 0 0 2 2 0 0 0 0 | * 8 * * * * * * | 1 1 0 0
xo .. xo ..&#x ♦ 4 1 | 2 2 4 0 0 | 1 0 2 0 2 0 0 0 | * * 8 * * * * * | 1 0 1 0
xo .. .. ox&#x ♦ 2 2 | 1 0 4 0 1 | 0 0 2 0 0 2 0 0 | * * * 8 * * * * | 0 1 1 0
.. ox xo ..&#x ♦ 2 2 | 0 1 4 1 0 | 0 0 0 2 2 0 0 0 | * * * * 8 * * * | 1 0 0 1
.. ox .. ox&#x ♦ 1 4 | 0 0 4 2 2 | 0 0 0 2 0 2 1 0 | * * * * * 8 * * | 0 1 0 1
.. .. xo4ox&#x ♦ 4 4 | 0 4 8 0 4 | 0 1 0 0 4 4 0 1 | * * * * * * 4 * | 0 0 1 1
.. .x .o4.x ♦ 0 8 | 0 0 0 4 8 | 0 0 0 0 0 0 4 2 | * * * * * * * 1 | 0 0 0 2
---------------+-----+------------+---------------------+-----------------+--------
xo ox xo ..&#x ♦ 4 2 | 2 2 8 1 0 | 1 0 4 4 4 0 0 0 | 0 2 2 0 2 0 0 0 | 4 * * *
xo ox .. ox&#x ♦ 2 4 | 1 0 8 2 2 | 0 0 4 4 0 4 1 0 | 0 2 0 2 0 2 0 0 | * 4 * *
xo .. xo4ox&#x ♦ 8 4 | 4 8 16 0 4 | 4 2 8 0 8 8 0 1 | 1 0 4 4 0 0 2 0 | * * 2 *
.. ox xo4ox&#x ♦ 4 8 | 0 4 16 4 8 | 0 1 0 8 8 8 4 2 | 0 0 0 0 4 4 2 1 | * * * 2
or o. o. o.4o. & | 16 | 1 2 4 | 2 1 6 6 | 1 2 5 4 2 | 3 3 -----------------+----+----------+------------+--------------+----- x. .. .. .. & | 2 | 8 * * | 2 0 4 0 | 1 2 4 2 0 | 3 2 .. .. x. .. & | 2 | * 16 * | 1 1 0 2 | 1 0 2 1 2 | 1 3 oo oo oo4oo&#x | 2 | * * 32 | 0 0 2 2 | 0 1 2 2 1 | 2 2 -----------------+----+----------+------------+--------------+----- x. .. x. .. & | 4 | 2 2 0 | 8 * * * | 1 0 2 0 0 | 1 2 .. .. x.4o. & | 4 | 0 4 0 | * 4 * * | 1 0 0 0 2 | 0 3 xo .. .. ..&#x & | 3 | 1 0 2 | * * 32 * | 0 1 1 1 0 | 2 1 .. .. xo ..&#x & | 3 | 0 1 2 | * * * 32 | 0 0 1 1 1 | 1 2 -----------------+----+----------+------------+--------------+----- x. .. x.4o. & ♦ 8 | 4 8 0 | 4 2 0 0 | 2 * * * * | 0 2 xo ox .. ..&#x ♦ 4 | 2 0 4 | 0 0 4 0 | * 8 * * * | 2 0 xo .. xo ..&#x & ♦ 5 | 2 2 4 | 1 0 2 2 | * * 16 * * | 1 1 xo .. .. ox&#x & ♦ 4 | 1 1 4 | 0 0 2 2 | * * * 16 * | 1 1 .. .. xo4ox&#x ♦ 8 | 0 8 8 | 0 2 0 8 | * * * * 4 | 0 2 -----------------+----+----------+------------+--------------+----- xo ox xo ..&#x & ♦ 6 | 3 2 8 | 1 0 8 4 | 0 2 2 2 0 | 8 * xo .. xo4ox&#x & ♦ 12 | 4 12 16 | 4 4 8 16 | 1 0 4 4 2 | * 4
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