- general duoprisms:
- n,m-dip 2n,m-dip 5,n-dip 10,n-dip
- general polytopal classes:
- bistratic lace towers
links
| Acronym | padedip |
| Name | pentagon - decagon duoprism |
| Circumradius | sqrt[(10+3 sqrt(5))/5] = 1.828016 |
| Volume | 25[2+sqrt(5)]/8 = 13.237712 |
| General of army | (is itself convex) |
| Colonel of regiment | (is itself locally convex) |
| Dihedral angles | |
| Face vector | 50, 100, 65, 15 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
x5o x10o . . . . | 50 | 2 2 | 1 4 1 | 2 2 ---------+----+-------+---------+----- x . . . | 2 | 50 * | 1 2 0 | 2 1 . . x . | 2 | * 50 | 0 2 1 | 1 2 ---------+----+-------+---------+----- x5o . . | 5 | 5 0 | 10 * * | 2 0 x . x . | 4 | 2 2 | * 50 * | 1 1 . . x10o | 10 | 0 10 | * * 5 | 0 2 ---------+----+-------+---------+----- x5o x . ♦ 10 | 10 5 | 2 5 0 | 10 * x . x10o ♦ 20 | 10 20 | 0 10 2 | * 5
x5o x5x . . . . | 50 | 2 1 1 | 1 2 2 1 | 1 1 2 --------+----+----------+------------+------ x . . . | 2 | 50 * * | 1 1 1 0 | 1 1 1 . . x . | 2 | * 25 * | 0 2 0 1 | 1 0 2 . . . x | 2 | * * 25 | 0 0 2 1 | 0 1 2 --------+----+----------+------------+------ x5o . . | 5 | 5 0 0 | 10 * * * | 1 1 0 x . x . | 4 | 2 2 0 | * 25 * * | 1 0 1 x . . x | 4 | 2 0 2 | * * 25 * | 0 1 1 . . x5x | 10 | 0 5 5 | * * * 5 | 0 0 2 --------+----+----------+------------+------ x5o x . ♦ 10 | 10 5 0 | 2 5 0 0 | 5 * * x5o . x ♦ 10 | 10 0 5 | 2 0 5 0 | * 5 * x . x5x ♦ 20 | 10 10 10 | 0 5 5 2 | * * 5
ofx xxx10ooo&#xt → height(1,2) = sqrt[(5-sqrt(5))/8] = 0.587785
height(2,3) = sqrt[(5+sqrt(5))/8] = 0.951057
({10} || pseudo (f,x)-dip || dip)
o.. o..10o.. | 10 * * | 2 2 0 0 0 0 | 1 1 4 0 0 0 0 | 2 2 0 0
.o. .o.10.o. | * 20 * | 0 1 2 1 0 0 | 0 1 2 1 2 0 0 | 2 1 1 0
..o ..o10..o | * * 20 | 0 0 0 1 1 2 | 0 1 0 0 2 2 1 | 2 0 1 1
-----------------+----------+-------------------+-------------------+---------
... x.. ... | 2 0 0 | 10 * * * * * | 1 0 2 0 0 0 0 | 1 2 0 0
oo. oo.10oo.&#x | 1 1 0 | * 20 * * * * | 0 1 2 0 0 0 0 | 2 1 0 0
... .x. ... | 0 2 0 | * * 20 * * * | 0 0 1 1 1 0 0 | 1 1 1 0
.oo .oo10.oo&#x | 0 1 1 | * * * 20 * * | 0 1 0 0 2 0 0 | 2 0 1 0
..x ... ... | 0 0 2 | * * * * 10 * | 0 1 0 0 0 2 0 | 2 0 0 1
... ..x ... | 0 0 2 | * * * * * 20 | 0 0 0 0 1 1 1 | 1 0 1 1
-----------------+----------+-------------------+-------------------+---------
... x..10o.. | 10 0 0 | 10 0 0 0 0 0 | 1 * * * * * * | 0 2 0 0
ofx ... ...&#xt | 1 2 2 | 0 2 0 2 1 0 | * 10 * * * * * | 2 0 0 0
... xx. ...&#x | 2 2 0 | 1 2 1 0 0 0 | * * 20 * * * * | 1 1 0 0
... .x.10.o. | 0 10 0 | 0 0 10 0 0 0 | * * * 2 * * * | 0 1 1 0
... .xx ...&#x | 0 2 2 | 0 0 1 2 0 1 | * * * * 20 * * | 1 0 1 0
..x ..x ... | 0 0 4 | 0 0 0 0 2 2 | * * * * * 10 * | 1 0 0 1
... ..x10..o | 0 0 10 | 0 0 0 0 0 10 | * * * * * * 2 | 0 0 1 1
-----------------+----------+-------------------+-------------------+---------
ofx xxx ...&#xt ♦ 2 4 4 | 1 4 2 4 2 2 | 0 2 2 0 2 1 0 | 10 * * *
... xx.10oo.&#x ♦ 10 10 0 | 10 10 10 0 0 0 | 1 0 10 1 0 0 0 | * 2 * *
... .xx10.oo&#x ♦ 0 10 10 | 0 0 10 10 0 10 | 0 0 0 1 10 0 1 | * * 2 *
..x ..x10..o ♦ 0 0 20 | 0 0 0 0 10 20 | 0 0 0 0 0 10 2 | * * * 1
ofx xxx5xxx&#xt → height(1,2) = sqrt[(5-sqrt(5))/8] = 0.587785
height(2,3) = sqrt[(5+sqrt(5))/8] = 0.951057
({10} || pseudo (f,x)-dip || dip)
o.. o..5o.. | 10 * * | 1 1 2 0 0 0 0 0 0 | 1 1 2 2 0 0 0 0 0 0 | 1 1 2 0 0
.o. .o.5.o. | * 20 * | 0 0 1 1 1 1 0 0 0 | 0 1 1 1 1 1 1 0 0 0 | 1 1 1 1 0
..o ..o5..o | * * 20 | 0 0 0 0 0 1 1 1 1 | 0 1 0 0 0 1 1 1 1 1 | 1 1 0 1 1
----------------+----------+--------------------------+--------------------------+----------
... x.. ... | 2 0 0 | 5 * * * * * * * * | 1 0 2 0 0 0 0 0 0 0 | 1 0 2 0 0
... ... x.. | 2 0 0 | * 5 * * * * * * * | 1 0 0 2 0 0 0 0 0 0 | 0 1 2 0 0
oo. oo.5oo.&#x | 1 1 0 | * * 20 * * * * * * | 0 1 1 1 0 0 0 0 0 0 | 1 1 1 0 0
... .x. ... | 0 2 0 | * * * 10 * * * * * | 0 0 1 0 1 1 0 0 0 0 | 1 0 1 1 0
... ... .x. | 0 2 0 | * * * * 10 * * * * | 0 0 0 1 1 0 1 0 0 0 | 0 1 1 1 0
.oo .oo5.oo&#x | 0 1 1 | * * * * * 20 * * * | 0 1 0 0 0 1 1 0 0 0 | 1 1 0 1 0
..x ... ... | 0 0 2 | * * * * * * 10 * * | 0 1 0 0 0 0 0 1 1 0 | 1 1 0 0 1
... ..x ... | 0 0 2 | * * * * * * * 10 * | 0 0 0 0 0 1 0 1 0 1 | 1 0 0 1 1
... ... ..x | 0 0 2 | * * * * * * * * 10 | 0 0 0 0 0 0 1 0 1 1 | 0 1 0 1 1
----------------+----------+--------------------------+--------------------------+----------
... x..5x.. | 10 0 0 | 5 5 0 0 0 0 0 0 0 | 1 * * * * * * * * * | 0 0 2 0 0
ofx ... ...&#xt | 1 2 2 | 0 0 2 0 0 2 1 0 0 | * 10 * * * * * * * * | 1 1 0 0 0
... xx. ...&#x | 2 2 0 | 1 0 2 1 0 0 0 0 0 | * * 10 * * * * * * * | 1 0 1 0 0
... ... xx.&#x | 2 2 0 | 0 1 2 0 1 0 0 0 0 | * * * 10 * * * * * * | 0 1 1 0 0
... .x.5.x. | 0 10 0 | 0 0 0 5 5 0 0 0 0 | * * * * 2 * * * * * | 0 0 1 1 0
... .xx ...&#x | 0 2 2 | 0 0 0 1 0 2 0 1 0 | * * * * * 10 * * * * | 1 0 0 1 0
... ... .xx&#x | 0 2 2 | 0 0 0 0 1 2 0 0 1 | * * * * * * 10 * * * | 0 1 0 1 0
..x ..x ... | 0 0 4 | 0 0 0 0 0 0 2 2 0 | * * * * * * * 5 * * | 1 0 0 0 1
..x ... ..x | 0 0 4 | 0 0 0 0 0 0 2 0 2 | * * * * * * * * 5 * | 0 1 0 0 1
... ..x5..x | 0 0 10 | 0 0 0 0 0 0 0 5 5 | * * * * * * * * * 2 | 0 0 0 1 1
----------------+----------+--------------------------+--------------------------+----------
ofx xxx ...&#xt ♦ 2 4 4 | 1 0 4 2 0 4 2 2 0 | 0 2 2 0 0 2 0 1 0 0 | 5 * * * *
ofx ... xxx&#xt ♦ 2 4 4 | 0 1 4 0 2 4 2 0 2 | 0 2 0 2 0 0 2 0 1 0 | * 5 * * *
... xx.5xx.&#x ♦ 10 10 0 | 5 5 10 5 5 0 0 0 0 | 1 0 5 5 1 0 0 0 0 0 | * * 2 * *
... .xx5.xx&#x ♦ 0 10 10 | 0 0 0 5 5 10 0 5 5 | 0 0 0 0 1 5 5 0 0 1 | * * * 2 *
..x ..x5..x ♦ 0 0 20 | 0 0 0 0 0 0 10 10 10 | 0 0 0 0 0 0 0 5 5 2 | * * * * 1
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