©
in approx. ASCII-art
x5/2o x5/2o -- x x5/2o (stip) o5/2x o5/2x -- x o5/2x (gyro stip †) | | | +-- s2s5/2s (stap) +---------- s2s5/2s (stap)
- general antiprism-prisms:
- n/d-appip
- general polytopal classes:
- segmentochora
links
| Acronym | stappip |
| Name | pentagramic-antiprism prism |
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| Circumradius | sqrt[(25+sqrt(5))/40] = 0.825168 |
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Lace city in approx. ASCII-art |
x5/2o x5/2o -- x x5/2o (stip) o5/2x o5/2x -- x o5/2x (gyro stip †) | | | +-- s2s5/2s (stap) +---------- s2s5/2s (stap) |
| Face vector | 20, 50, 44, 14 |
| Confer |
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External links |
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† Just as in stap x5/2o and o5/2x had in effect the very same orientation (but X-shaped lacings), the mutual gyration of the stips results here too in an alignment of effectively the same orientation above each other. Only the respective displacement happens to be a bit narrower than that of a mere straight prism stacking.
Incidence matrix according to Dynkin symbol
x s2s5/2s . demi( . . . ) | 20 | 1 1 1 2 | 1 1 2 1 3 | 1 3 1 ------------------+----+-------------+-------------+------- x demi( . . . ) | 2 | 10 * * * | 1 1 2 0 0 | 1 3 0 . s2s . | 2 | * 10 * * | 1 0 0 0 2 | 0 2 1 . s 2 s | 2 | * * 10 * | 0 1 0 0 2 | 0 2 1 . sefa( . s5/2s ) | 2 | * * * 20 | 0 0 1 1 1 | 1 1 1 ------------------+----+-------------+-------------+------- x s2s . | 4 | 2 2 0 0 | 5 * * * * | 0 2 0 x s 2 s | 4 | 2 0 2 0 | * 5 * * * | 0 2 0 x sefa( . s5/2s ) | 4 | 2 0 0 2 | * * 10 * * | 1 1 0 . . s5/2s ♦ 5 | 0 0 0 5 | * * * 4 * | 1 0 1 . sefa( s2s5/2s ) | 3 | 0 1 1 1 | * * * * 20 | 0 1 1 ------------------+----+-------------+-------------+------- x . s5/2s ♦ 10 | 5 0 0 10 | 0 0 5 2 0 | 2 * * x sefa( s2s5/2s ) ♦ 6 | 3 2 2 2 | 1 1 1 0 2 | * 10 * . s2s5/2s ♦ 10 | 0 5 5 10 | 0 0 0 2 10 | * * 2
x β2β5o . demi( . . . ) | 20 | 1 2 2 | 2 2 1 3 | 1 3 1 ----------------+----+----------+------------+------- x demi( . . . ) | 2 | 10 * * | 2 2 0 0 | 1 3 0 . β2β . | 2 | * 20 * | 1 0 0 2 | 0 2 1 . sefa( . β5o ) | 2 | * * 20 | 0 1 1 1 | 1 1 1 ----------------+----+----------+------------+------- x β2β . | 4 | 2 2 0 | 10 * * * | 0 2 0 x sefa( . β5o ) | 4 | 2 0 2 | * 10 * * | 1 1 0 . . β5o ♦ 5 | 0 0 5 | * * 4 * | 1 0 1 . sefa( β2β5o ) | 3 | 0 2 1 | * * * 20 | 0 1 1 ----------------+----+----------+------------+------- x . β5o ♦ 10 | 5 0 10 | 0 5 2 0 | 2 * * x sefa( β2β5o ) ♦ 6 | 3 4 2 | 2 1 0 2 | * 10 * . β2β5o ♦ 10 | 0 10 10 | 0 0 2 10 | * * 2 starting figure: x x x5o
xx xo5/2ox&#x → height = sqrt[(sqrt(5)-1)/2] = 0.786151
(stip || gyro stip)
o. o.5/2o. | 10 * | 1 2 2 0 0 | 2 1 2 2 1 0 0 | 1 2 1 1 0
.o .o5/2.o | * 10 | 0 0 2 1 2 | 0 0 2 1 2 2 1 | 0 1 2 1 1
--------------+-------+--------------+------------------+----------
x. .. .. | 2 0 | 5 * * * * | 2 0 2 0 0 0 0 | 1 2 1 0 0
.. x. .. | 2 0 | * 10 * * * | 1 1 0 1 0 0 0 | 1 1 0 1 0
oo oo5/2oo&#x | 1 1 | * * 20 * * | 0 0 1 1 1 0 0 | 0 1 1 1 0
.x .. .. | 0 2 | * * * 5 * | 0 0 2 0 0 2 0 | 0 1 2 0 1
.. .. .x | 0 2 | * * * * 10 | 0 0 0 0 1 1 1 | 0 0 1 1 1
--------------+-------+--------------+------------------+----------
x. x. .. | 4 0 | 2 2 0 0 0 | 5 * * * * * * | 1 1 0 0 0
.. x.5/2o. | 5 0 | 0 5 0 0 0 | * 2 * * * * * | 1 0 0 1 0
xx .. ..&#x | 2 2 | 1 0 2 1 0 | * * 10 * * * * | 0 1 1 0 0
.. xo ..&#x | 2 1 | 0 1 2 0 0 | * * * 10 * * * | 0 1 0 1 0
.. .. ox&#x | 1 2 | 0 0 2 0 1 | * * * * 10 * * | 0 0 1 1 0
.x .. .x | 0 4 | 0 0 0 2 2 | * * * * * 5 * | 0 0 1 0 1
.. .o5/2.x | 0 5 | 0 0 0 0 5 | * * * * * * 2 | 0 0 0 1 1
--------------+-------+--------------+------------------+----------
x. x.5/2o. ♦ 10 0 | 5 10 0 0 0 | 5 2 0 0 0 0 0 | 1 * * * *
xx xo ..&#x ♦ 4 2 | 2 2 4 1 0 | 1 0 2 2 0 0 0 | * 5 * * *
xx .. ox&#x ♦ 2 4 | 1 0 4 2 2 | 0 0 2 0 2 1 0 | * * 5 * *
.. xo5/2ox&#x ♦ 5 5 | 0 5 10 0 5 | 0 1 0 5 5 0 1 | * * * 2 *
.x .o5/2.x ♦ 0 10 | 0 0 0 5 10 | 0 0 0 0 0 5 2 | * * * * 1
s2s5/2s || s2s5/2s → height = 1 (stap || stap) demi( . . . ) | 10 * | 1 1 2 1 0 0 0 | 1 3 1 1 2 0 0 | 1 1 3 0 demi( . . . ) | * 10 | 0 0 0 1 1 1 2 | 0 0 1 1 2 1 3 | 0 1 3 1 ----------------------------------+-------+------------------+------------------+--------- s2s . | 2 0 | 5 * * * * * * | 0 2 1 0 0 0 0 | 1 0 1 0 s 2 s | 2 0 | * 5 * * * * * | 0 2 0 1 0 0 0 | 1 0 1 0 sefa( . s5/2s ) | 2 0 | * * 10 * * * * | 1 1 0 0 1 0 0 | 1 1 1 0 demi( . . . ) || demi( . . . ) | 1 1 | * * * 10 * * * | 0 0 1 1 2 0 0 | 0 1 3 0 s2s . | 0 2 | * * * * 5 * * | 0 0 1 0 0 0 2 | 0 0 2 1 s 2 s | 0 2 | * * * * * 5 * | 0 0 0 1 0 0 2 | 0 0 2 1 sefa( . s5/2s ) | 0 2 | * * * * * * 10 | 0 0 0 0 1 1 1 | 0 1 1 1 ----------------------------------+-------+------------------+------------------+--------- . s5/2s ♦ 5 0 | 0 0 5 0 0 0 0 | 2 * * * * * * | 1 1 0 0 sefa( s2s5/2s ) | 3 0 | 1 1 1 0 0 0 0 | * 10 * * * * * | 1 0 1 0 s2s . || s2s . | 2 2 | 1 0 0 2 1 0 0 | * * 5 * * * * | 0 0 2 0 s 2 s || s 2 s | 2 2 | 0 1 0 2 0 1 0 | * * * 5 * * * | 0 0 2 0 sefa( . s5/2s ) || sefa( . s5/2s ) | 2 2 | 0 0 1 2 0 0 1 | * * * * 10 * * | 0 1 1 0 . s5/2s ♦ 0 5 | 0 0 0 0 0 0 5 | * * * * * 2 * | 0 1 0 1 sefa( s2s5/2s ) | 0 3 | 0 0 0 0 1 1 1 | * * * * * * 10 | 0 0 1 1 ----------------------------------+-------+------------------+------------------+--------- s2s5/2s ♦ 10 0 | 5 5 10 0 0 0 0 | 2 10 0 0 0 0 0 | 1 * * * . s5/2s || . s5/2s ♦ 5 5 | 0 0 5 5 0 0 5 | 1 0 0 0 5 1 0 | * 2 * * sefa( s2s5/2s ) || sefa( s2s5/2s ) ♦ 3 3 | 1 1 1 3 1 1 1 | 0 1 1 1 1 0 1 | * * 10 * s2s5/2s ♦ 0 10 | 0 0 0 0 5 5 10 | 0 0 0 0 0 2 10 | * * * 1
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