Acronym | tetu |
Name |
axially-tetrahedral ursachoron ofx3xoo3ooo&#xt, tet-based ursulate, vertex figure of sadit |
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Circumradius | 1 |
Inradius wrt. tet | sqrt(5/8) = 0.790569 |
Inradius wrt. oct | 1/sqrt(2) = 0.707107 |
Inradius wrt. teddi | [sqrt(5)-1]/4 = 0.309017 |
Lace city in approx. ASCII-art |
o o x x o o f o o f x o o x |
o3o o3o x3o x3o f3o o3x | |
Coordinates |
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Volume | [28+13 sqrt(5)]/96 = 0.594468 |
Surface | [30+9 sqrt(2)+14 sqrt(5)]/12 = 6.169406 |
Face vector | 14, 34, 30, 10 |
Confer |
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External links |
The existance of a circumradius shows that this CRF polychoron even is orbiform.
When one of the 4 teddies gets augmented by {3}||teddi (e.g. in the second lace city above at the lower left) then this polychoron becomes xfox oxfo3ooox&#xt (the 3-mibdies-laced wedge).
Incidence matrix according to Dynkin symbol
ofx3xoo3ooo&#xt → height(1,2) = sqrt[3+sqrt(5)]/4 = 0.572061 height(2,3) = sqrt[7+3 sqrt(5)]/4 = 0.925615 (oct || pseudo f-tet || tet) o..3o..3o.. | 6 * * | 4 2 0 0 | 2 2 1 4 0 | 1 2 2 0 .o.3.o.3.o. | * 4 * | 0 3 1 0 | 0 0 3 3 0 | 0 3 1 0 ..o3..o3..o | * * 4 | 0 0 1 3 | 0 0 3 0 3 | 0 3 0 1 ----------------+-------+-----------+------------+-------- ... x.. ... | 2 0 0 | 12 * * * | 1 1 0 1 0 | 1 1 1 0 oo.3oo.3oo.&#x | 1 1 0 | * 12 * * | 0 0 1 2 0 | 0 2 1 0 .oo3.oo3.oo&#x | 0 1 1 | * * 4 * | 0 0 3 0 0 | 0 3 0 0 ..x ... ... | 0 0 2 | * * * 6 | 0 0 1 0 2 | 0 2 0 1 ----------------+-------+-----------+------------+-------- o..3x.. ... | 3 0 0 | 3 0 0 0 | 4 * * * * | 1 1 0 0 ... x..3o.. | 3 0 0 | 3 0 0 0 | * 4 * * * | 1 0 1 0 ofx ... ...&#xt | 1 2 2 | 0 2 2 1 | * * 6 * * | 0 2 0 0 ... xo. ...&#x | 2 1 0 | 1 2 0 0 | * * * 12 * | 0 1 1 0 ..x3..o ... | 0 0 3 | 0 0 0 3 | * * * * 4 | 0 1 0 1 ----------------+-------+-----------+------------+-------- o..3x..3o.. ♦ 6 0 0 | 12 0 0 0 | 4 4 0 0 0 | 1 * * * ofx3xoo ...&#xt ♦ 3 3 3 | 3 6 3 3 | 1 0 3 3 1 | * 4 * * ... xo.3oo.&#x ♦ 3 1 0 | 3 3 0 0 | 0 1 0 3 0 | * * 4 * ..x3..o3..o ♦ 0 0 4 | 0 0 0 6 | 0 0 0 0 4 | * * * 1
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