Acronym | peppyp, K-4.38 |
Name |
pentagon-pyramidal prism, J2 prism, line || pip |
Segmentochoron display | |
Circumradius | sqrt[(7+sqrt(5))/8] = 1.074481 |
Dihedral angles | |
Face vector | 12, 26, 22, 8 |
Confer |
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External links |
As abstract polytope peppyp is isomorphic to stappyp, thereby replacing pentagons by pentagrams resp. replacing peppy by stappy and pip by stip.
Incidence matrix according to Dynkin symbol
xx ox5oo&#x → height = sqrt((5-sqrt(5))/10) = 0.525731
(line || pip)
o. o.5o. | 2 * | 1 5 0 0 | 5 5 0 0 | 5 1 0
.o .o5.o | * 10 | 0 1 1 2 | 1 2 2 1 | 2 1 1
------------+------+-----------+----------+------
x. .. .. | 2 0 | 1 * * * | 5 0 0 0 | 5 0 0
oo oo5oo&#x | 1 1 | * 10 * * | 1 2 0 0 | 2 1 0
.x .. .. | 0 2 | * * 5 * | 1 0 2 0 | 2 0 1
.. .x .. | 0 2 | * * * 10 | 0 1 1 1 | 1 1 1
------------+------+-----------+----------+------
xx .. ..&#x | 2 2 | 1 2 1 0 | 5 * * * | 2 0 0
.. ox ..&#x | 1 2 | 0 2 0 1 | * 10 * * | 1 1 0
.x .x .. | 0 4 | 0 0 2 2 | * * 5 * | 1 0 1
.. .x5.o | 0 5 | 0 0 0 5 | * * * 2 | 0 1 1
------------+------+-----------+----------+------
xx ox ..&#x ♦ 2 4 | 1 4 2 2 | 2 2 1 0 | 5 * *
.. ox5oo&#x ♦ 1 5 | 0 5 0 5 | 0 5 0 1 | * 2 *
.x .x5.o ♦ 0 10 | 0 0 5 10 | 0 0 5 2 | * * 1
peppy || peppy → height = 1
1 * * * | 5 1 0 0 0 0 | 5 5 0 0 0 0 | 1 5 0 0 top-tip
* 5 * * | 1 0 2 1 0 0 | 2 1 1 0 0 0 | 1 2 1 0 top-base
* * 1 * | 0 1 0 0 5 0 | 0 5 0 0 5 0 | 0 5 0 1 bottom-tip
* * * 5 | 0 0 0 1 1 2 | 0 1 0 2 2 1 | 0 2 1 1 bottom-base
----------+-------------+-------------+--------
1 1 0 0 | 5 * * * * * | 2 1 0 0 0 0 | 1 2 0 0
1 0 1 0 | * 1 * * * * | 0 5 0 0 0 0 | 0 5 0 0
0 2 0 0 | * * 5 * * * | 1 0 1 1 0 0 | 1 1 1 0
0 1 0 1 | * * * 5 * * | 0 1 0 2 0 0 | 0 2 1 0
0 0 1 1 | * * * * 5 * | 0 1 0 0 2 0 | 0 2 0 1
0 0 0 2 | * * * * * 5 | 0 0 0 1 1 1 | 0 1 1 1
----------+-------------+-------------+--------
1 2 0 0 | 2 0 1 0 0 0 | 5 * * * * * | 1 1 0 0
1 1 1 1 | 1 1 0 1 1 0 | * 5 * * * * | 0 2 0 0
0 5 0 0 | 0 0 5 0 0 0 | * * 1 * * * | 1 0 1 0
0 2 0 2 | 0 0 1 2 0 1 | * * * 5 * * | 0 1 1 0
0 0 1 2 | 0 0 0 0 2 1 | * * * * 5 * | 0 1 0 1
0 0 0 5 | 0 0 0 0 0 5 | * * * * * 1 | 0 0 1 1
----------+-------------+-------------+--------
♦ 1 5 0 0 | 5 0 5 0 0 0 | 5 0 1 0 0 0 | 1 * * *
♦ 1 2 1 2 | 2 1 1 2 2 1 | 1 2 0 1 1 0 | * 5 * *
♦ 0 5 0 5 | 0 0 5 5 0 5 | 0 0 1 5 0 1 | * * 1 *
♦ 0 0 1 5 | 0 0 0 0 5 5 | 0 0 0 0 5 1 | * * * 1
oxxo5oooo&#xr → height(1,2) = height(3,4) = sqrt((5-sqrt(5))/10) = 0.525731 height(1,4) = height(2,3) = 1 ( (pt || {5}) || (pt || {5}) ) o...5o... | 1 * * * | 5 1 0 0 0 0 | 5 5 0 0 0 0 | 1 5 0 0 .o..5.o.. | * 5 * * | 1 0 2 1 0 0 | 2 1 1 2 0 0 | 1 2 1 0 ..o.5..o. | * * 5 * | 0 0 0 1 2 1 | 0 1 0 2 1 2 | 0 2 1 1 ...o5...o | * * * 1 | 0 1 0 0 0 5 | 0 5 0 0 0 5 | 0 5 0 1 --------------+---------+-------------+-------------+-------- oo..5oo..&#x | 1 1 0 0 | 5 * * * * * | 2 1 0 0 0 0 | 1 2 0 0 o..o5o..o&#x | 1 0 0 1 | * 1 * * * * | 0 5 0 0 0 0 | 0 5 0 0 .x.. .... | 0 2 0 0 | * * 5 * * * | 1 0 1 1 0 0 | 1 1 1 0 .oo.5.oo.&#x | 0 1 1 0 | * * * 5 * * | 0 1 0 2 0 0 | 0 2 1 0 ..x. .... | 0 0 2 0 | * * * * 5 * | 0 0 0 1 1 1 | 0 1 1 1 ..oo5..oo&#x | 0 0 1 1 | * * * * * 5 | 0 1 0 0 0 2 | 0 2 0 1 --------------+---------+-------------+-------------+-------- ox.. ....&#x | 1 2 0 0 | 2 0 1 0 0 0 | 5 * * * * * | 1 1 0 0 oooo5oooo&#xr | 1 1 1 1 | 1 1 0 1 0 1 | * 5 * * * * | 0 2 0 0 .x..5.o.. | 0 5 0 0 | 0 0 5 0 0 0 | * * 1 * * * | 1 0 1 0 .xx. ....&#x | 0 2 2 0 | 0 0 1 2 1 0 | * * * 5 * * | 0 1 1 0 ..x.5..o. | 0 0 5 0 | 0 0 0 0 5 0 | * * * * 1 * | 0 0 1 1 ..xo ....&#x | 0 0 2 1 | 0 0 0 0 1 2 | * * * * * 5 | 0 1 0 1 --------------+---------+-------------+-------------+-------- ox..5oo..&#x ♦ 1 5 0 0 | 5 0 5 0 0 0 | 5 0 1 0 0 0 | 1 * * * oxxo ....&#xr ♦ 1 2 2 1 | 2 1 1 2 1 2 | 1 2 0 1 0 1 | * 5 * * .xx.5.oo.&#x ♦ 0 5 5 0 | 0 0 5 5 5 0 | 0 0 1 5 1 0 | * * 1 * ..xo5..oo&#x ♦ 0 0 5 1 | 0 0 0 0 5 5 | 0 0 0 0 1 5 | * * * 1
o(xo)x5o(oo)o&#xt (pt || ({5} || pt) || para {5}) o(..).5o(..). | 1 * * * | 5 1 0 0 0 0 | 5 5 0 0 0 0 | 1 5 0 0 .(o.).5.(o.). | * 5 * * | 1 0 2 1 0 0 | 2 1 1 2 0 0 | 1 2 1 0 .(.o).5.(.o). | * * 1 * | 0 1 0 0 5 0 | 0 5 0 0 5 0 | 0 5 0 1 .(..)o5.(..)o | * * * 5 | 0 0 0 1 1 2 | 0 1 0 2 2 1 | 0 2 1 1 ------------------+---------+-------------+-------------+-------- o(o.).5o(o.).&#x | 1 1 0 0 | 5 * * * * * | 2 1 0 0 0 0 | 1 2 0 0 o(.o).5o(.o).&#x | 1 0 1 0 | * 1 * * * * | 0 5 0 0 0 0 | 0 5 0 0 .(x.). .(..). | 0 2 0 0 | * * 5 * * * | 1 0 1 1 0 0 | 1 1 1 0 .(o.)o5.(o.)o&#x | 0 1 0 1 | * * * 5 * * | 0 1 0 2 0 0 | 0 2 1 0 .(.o)o5.(.o)o&#x | 0 0 1 1 | * * * * 5 * | 0 1 0 0 2 0 | 0 2 0 1 .(..)x .(..). | 0 0 0 2 | * * * * * 5 | 0 0 0 1 1 1 | 0 1 1 1 ------------------+---------+-------------+-------------+-------- o(x.). .(..).&#x | 1 2 0 0 | 2 0 1 0 0 0 | 5 * * * * * | 1 1 0 0 o(oo)o5o(oo)o&#xt | 1 1 1 1 | 1 1 0 1 1 0 | * 5 * * * * | 0 2 0 0 .(x.).5.(o.). | 0 5 0 0 | 0 0 5 0 0 0 | * * 1 * * * | 1 0 1 0 .(x.)x .(..).&#x | 0 2 0 2 | 0 0 1 2 0 1 | * * * 5 * * | 0 1 1 0 .(.o)x .(..).&#x | 0 0 1 2 | 0 0 0 0 2 1 | * * * * 5 * | 0 1 0 1 .(..)x5.(..)o | 0 0 0 5 | 0 0 0 0 0 5 | * * * * * 1 | 0 0 1 1 ------------------+---------+-------------+-------------+-------- o(x.).5o(o.).&#x ♦ 1 5 0 0 | 5 0 5 0 0 0 | 5 0 1 0 0 0 | 1 * * * o(xo)x .(..).&#xt ♦ 1 2 1 2 | 2 1 1 2 2 1 | 1 2 0 1 1 0 | * 5 * * .(x.)x5.(o.)o&#x ♦ 0 5 0 5 | 0 0 5 5 0 5 | 0 0 1 5 0 1 | * * 1 * .(.o)x5.(.o)o&#x ♦ 0 0 1 5 | 0 0 0 0 5 5 | 0 0 0 0 5 1 | * * * 1
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