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Sage devel [[https://groups.google.com/forum/#!topic/sagedevel/QH_E14WHQ70discussion]] 
A Roadmap for Optimization and Polyhedral Geometry softwares interactions
(around Sage, (PyQ)Normaliz, SCIP, eantic, Polymake, and others)
This page is intended to describe the current status of development of Sage related to optimization and polyhedral geometry.
Future & Current Projects
 Extend the usage of Normaliz in Sage
 Extend the polyhedral geometry component of sage
 Polyhedral arrangements and complexes
Meetings
Sage Days 84 on Polytopes in Olot
Tickets
Here are some practical lists of tickets:
Tickets from the Sage Days 84 March 2017
Tickets from the IMA Coding Sprint  April 2018
Current tickets of the Geometry component
Metatickets
There are already a few metatickets related to this topic:
Polytopes, lattice (integer) point counting / enumeration, and their applications
Improvements to MixedIntegerLinearProgram, its backends, and InteractiveLinearProgram
To do
Test the algebraic polytopes #25097
Make Polyhedron_normaliz accept algebraic stuff, related to #25097 (adapt _init_from_Hrepresentation)
 Add known irrational polytope to the library of polytopes
repr of NumberFields (the parents) should indicate its embedding if there is one #21161 (this ticket will help in debugging and have good feedback)
 Thematic Tutorial for Py(Q)Normaliz installation/Usage in Sage
 Increase documentation in Py(Q)Normaliz
Deprecate the opacity argument for plot3d and use alpha #21984
Make Ehrhart (quasi)polynomial accessible through normaliz (and consisten with the current one) #18957
Progress Report Timeline
April 2018
Sage
Here are improvements realized to objects related to polyhedron in Sage:
Thematic tutorial on polyhedron in Sage #22572
Make features of normaliz accessible #25091
number_field_elements_from_algebraics should create embedded number field elements #20181
 Helper functions in the normaliz backend
Change error message in construction of polyhedron object #24835
Improve the output of repr_pretty for Polyhedron #24837
Implement stacking onto a face of a polyhedron #24847
Implement join of polytopes #24848
Implement one point suspension and face split of polyhedron #24886
The polar of a polyhedron should carry the backend used #25081
Construct RationalPolyhedralFan from possibly overlapping cones #25122
polygon3d ignores the "alpha" (and equivalent "opacity") argument #25095
(Q)Normaliz
http://normaliz.uniosnabrueck.de
Upgrade normaliz to 3.5.3 and pynormaliz to 1.12 #22984
Algebraic polytope using eantic #25097
getProjectionCone might segfault https://github.com/Normaliz/Normaliz/issues/180
BadInputException for ProjectCone https://github.com/Normaliz/Normaliz/issues/181
Unified getter https://github.com/Normaliz/Normaliz/pull/182
Py(Q)Normaliz
https://pypi.python.org/pypi/PyNormaliz https://github.com/Normaliz/PyNormaliz
Upgrade normaliz to 3.5.3 and pynormaliz to 1.12 #22984
Upgraded pynormaliz to 1.16 https://github.com/Normaliz/PyNormaliz
Started PyQNormaliz. https://github.com/sebasguts/PyQNormaliz
PyScipOpt
https://github.com/SCIPInterfaces/PySCIPOpt
Sage devel discussion
Polymake
Upgrade polymake to version 3.2r2 (current interface breaks) #24905
A list of other Polyhedral Geometry softwares
What are other softwares dealing with polyhedral geometry? Here is a nonexhaustive list.
 Maple:
https://www.maplesoft.com/support/help/Maple/view.aspx?path=PolyhedralSets%2fPolyhedralSet (seems to be only rational and implemented in 2015).
http://qhull.org/ (seems old?)
https://www.maplesoft.com/products/maple/new_features/Maple2018/ComputationalGeometry.aspx
https://www.maplesoft.com/support/help/Maple/view.aspx?path=PolyhedralSets
 CGAL:
 A paper:
Jing & Maza https://dl.acm.org/citation.cfm?id=3177798
 Matlab:
 Matematica: